<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="15" minor="0"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="true"><Hide name="Group Range"/><Hide name="Section Range"/><Hide name="Table Borders"/><Hide name="Annotations"/></View-Properties>
<MapleNet-Properties elisiondigitsbefore="100" labelling="true" indentamount="4" elisiontermsthreshold="10000" ansi="false" errorbreak="1" useclientjvm="true" echo="1" imaginaryunit="I" labelwidth="20" contextmenusize="automatic" plotdriver="opengl" elisiondigitsafter="100" plotoutput="terminal" helpbrowser="standard" rtablesize="10" elisiontermsbefore="100" elisiondigitsthreshold="10000" typesetting="standard" plotdevice="inline" verboseproc="1" showassumed="1" errorcursor="false" longdelim="true" plotoptions="" quiet="false" elisiontermsafter="100" screenwidth="79" preplot="" prettyprint="3" displayprecision="-1" screenpixelheight="1200" warnlevel="3" screenheight="25" latexwidth="6.0" postplot="" prompt="&gt; " ShowLabels="true"/>
<Styles><Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Caption Reference" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Code" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[40,120,40]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="HyperlinkError" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Header and Footer" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Page Number" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 4" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="16" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="HyperlinkWarning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Caption Text" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="newline" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.3" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="HyperlinkError" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="HyperlinkWarning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
</Styles>
<Task-table>
    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table>
<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
</Annotation-table>
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action="click-event-handler">restart: mapler:=proc(a,b,c,A,B,C,K,L,M) local Y1,Y2,eq1,eq2,eq3,S,a1,b1,c1,p,q,P,Q,X1,X2;print(`\320\222 \320\270\321\201\321\205\320\276\320\264\320\275\320\276\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\320\265`);Y1:=a*x+b*y=c;Y2:=A*x^2+B*x*y+C*y^2+K*x+L*y=M;print(piecewise(Y1,``,Y2,``));print(`\320\277\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 - \320\273\320\270\320\275\320\265\320\271\320\275\320\276\320\265.`);print(`\320\222\321\213\321\200\320\260\320\267\320\270\320\274 \320\270\320\267 \320\275\320\265\320\263\320\276 \321\205 \321\207\320\265\321\200\320\265\320\267 \321\203 \320\270 \320\277\320\276\320\264\321\201\321\202\320\260\320\262\320\270\320\274 \320\262 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265:`);eq1:=x=(c-b*y)/a;eq2:=subs(x=(c-b*y)/a,lhs(Y2))-M=0;print(piecewise(eq1,``,eq2,``));print(`\320\232\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\277\320\276  \321\203  \320\277\321\200\320\270\320\262\320\265\320\264\321\221\320\274 \320\272 \321\201\321\202\320\260\320\275\320\264\320\260\321\200\321\202\320\275\320\276\320\274\321\203 \320\262\320\270\320\264\321\203:`);S:=simplify(eq2);a1:=coeff(lhs(S),y,2);b1:=coeff(lhs(S),y,1);c1:=coeff(lhs(S),y,0);p:=b1/a1;q:=c1/a1;P:=denom(p);Q:=denom(q);[a1,b1,c1];if P=1 and Q=1 then eq3:=sort(y^2+p*y+q)=0;print(%);print(`\320\230\321\201\320\272\320\276\320\274\321\213\320\265 \320\272\320\276\321\200\320\275\320\270:`);Y1:=(-p-sqrt(p^2-4*q))/2;Y2:=(-p+sqrt(p^2-4*q))/2;print(y[1]=Y1,y[2]=Y2);print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276:`);X1:=subs(y=Y1,(c-b*y)/a);X2:=subs(y=Y2,(c-b*y)/a);print(x[1]=X1,x[2]=X2);else eq3:=sort(a1*y^2+b1*y+c1)=0;print(%);print(`\320\230\321\201\320\272\320\276\320\274\321\213\320\265 \320\272\320\276\321\200\320\275\320\270:`);Y1:=(-b1-sqrt(b1^2-4*a1*c1))/2/a1;Y2:=(-b1+sqrt(b1^2-4*a1*c1))/2/a1;print(y[1]=Y1,y[2]=Y2);print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276:`);X1:=subs(y=Y1,(c-b*y)/a);X2:=subs(y=Y2,(c-b*y)/a);print(x[1]=X1,x[2]=X2); fi;print(`\320\237\320\265\321\200\320\265\321\205\320\276\320\264\321\213 \320\261\321\213\320\273\320\270 \321\200\320\260\320\262\320\275\320\276\321\201\320\270\320\273\321\214\320\275\321\213\320\274\320\270.`);print(`\320\236\320\242\320\222\320\225\320\242:`);print({x[1]=X1,y[1]=Y1});print({x[2]=X2,y[2]=Y2});end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart;mapler:=proc(a,b,c,A,B,C,K,L,M) local Y1,Y2,eq1,eq2,eq3,S,a1,b1,c1,p,q,P,Q,X1,X2;print(`\320\222 \320\270\321\201\321\205\320\276\320\264\320\275\320\276\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\320\265`);Y1:=a*x+b*y=c;Y2:=A*x^2+B*x*y+C*y^2+K*x+L*y=M;print(piecewise(Y1,``,Y2,``));print(`\320\277\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 - \320\273\320\270\320\275\320\265\320\271\320\275\320\276\320\265.`);print(`\320\222\321\213\321\200\320\260\320\267\320\270\320\274 \320\270\320\267 \320\275\320\265\320\263\320\276 \321\205 \321\207\320\265\321\200\320\265\320\267 \321\203 \320\270 \320\277\320\276\320\264\321\201\321\202\320\260\320\262\320\270\320\274 \320\262 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265:`);eq1:=x=(c-b*y)/a;eq2:=subs(x=(c-b*y)/a,lhs(Y2))-M=0;print(piecewise(eq1,``,eq2,``));print(`\320\232\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\277\320\276  \321\203  \320\277\321\200\320\270\320\262\320\265\320\264\321\221\320\274 \320\272 \321\201\321\202\320\260\320\275\320\264\320\260\321\200\321\202\320\275\320\276\320\274\321\203 \320\262\320\270\320\264\321\203:`);S:=simplify(eq2);a1:=coeff(lhs(S),y,2);b1:=coeff(lhs(S),y,1);c1:=coeff(lhs(S),y,0);p:=b1/a1;q:=c1/a1;P:=denom(p);Q:=denom(q);[a1,b1,c1];if P=1 and Q=1 then eq3:=sort(y^2+p*y+q)=0;print(%);print(`\320\230\321\201\320\272\320\276\320\274\321\213\320\265 \320\272\320\276\321\200\320\275\320\270:`);Y1:=(-p-sqrt(p^2-4*q))/2;Y2:=(-p+sqrt(p^2-4*q))/2;print(y[1]=Y1,y[2]=Y2);print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276:`);X1:=subs(y=Y1,(c-b*y)/a);X2:=subs(y=Y2,(c-b*y)/a);print(x[1]=X1,x[2]=X2);else eq3:=denom(a1)*sort(a1*y^2+b1*y+c1)=0;print(%);print(`\320\230\321\201\320\272\320\276\320\274\321\213\320\265 \320\272\320\276\321\200\320\275\320\270:`);Y1:=(-b1-sqrt(b1^2-4*a1*c1))/2/a1;Y2:=(-b1+sqrt(b1^2-4*a1*c1))/2/a1;print(y[1]=Y1,y[2]=Y2);print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276:`);X1:=subs(y=Y1,(c-b*y)/a);X2:=subs(y=Y2,(c-b*y)/a);print(x[1]=X1,x[2]=X2); fi;print(`\320\237\320\265\321\200\320\265\321\205\320\276\320\264\321\213 \320\261\321\213\320\273\320\270 \321\200\320\260\320\262\320\275\320\276\321\201\320\270\320\273\321\214\320\275\321\213\320\274\320\270.`);print(`\320\236\320\242\320\222\320\225\320\242:`);print({x[1]=X1,y[1]=Y1});print({x[2]=X2,y[2]=Y2});end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">mapler:=proc(a,b,c1,c2) local Y,Y1,Y2,n,A,B,c,d,x1,x2,S,y1,y2,m,C;print(`\320\222 \320\277\320\265\321\200\320\262\320\276\320\274 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\270 \321\201\320\270\321\201\321\202\320\265\320\274\321\213`);Y1:=1/a/x-1/b/y=c1;Y2:=b*y-a*x=c2;Y:=piecewise(Y1,``,Y2,``);print(%);print(`\321\201\320\273\320\276\320\266\320\270\320\274 \320\264\321\200\320\276\320\261\320\270 \320\262 \320\273\320\265\320\262\320\276\320\271 \320\265\320\263\320\276 \321\207\320\260\321\201\321\202\320\270:`);Y1:=(b*y-a*x)/(a*b*x*y)=c1;print(%);print(`\320\270 \320\270\321\201\320\277\320\276\320\273\321\214\320\267\321\203\320\265\320\274 \320\262\321\202\320\276\321\200\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);Y1:=c2/(a*b*x*y)=c1;print(%);Y1:=x*y=c2/(a*b*c1);print(`\320\242\320\276\320\263\320\264\320\260 \321\201\320\270\321\201\321\202\320\265\320\274\320\260 \320\274\320\276\320\266\320\265\321\202 \320\261\321\213\321\202\321\214 \320\277\320\265\321\200\320\265\320\277\320\270\321\201\320\260\320\275\320\260 \320\262 \320\262\320\270\320\264\320\265:`);Y2:=y=(a*x+c2)/b;print(piecewise(Y1,``,Y2,``));Y1:=x*(a*x+c2)/b=c2/(a*b*c1);print(`\320\230\320\267 \320\275\320\265\321\221 \320\277\320\276\320\273\321\203\321\207\320\260\320\265\320\274 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265  \320\262 \320\276\321\202\320\275\320\276\321\210\320\265\320\275\320\270\320\270  \321\205 :`);Y1:=sort(a*x^2/b+(c2/b)*x-c2/(a*b*c1))=0;print(%);n:=ilcm(denom(c2/a/b/c1),denom(a/b),denom(c2/b));m:=igcd(numer(c2/a/b/c1),numer(a/b),numer(c2/b));Y1:=lhs(Y1)*n/m=0;print(`\320\243\320\277\321\200\320\276\321\201\321\202\320\270\320\274 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265:`);print(Y1);A:=coeff(lhs(Y1),x,2);B:=coeff(lhs(Y1),x,1);C:=coeff(lhs(Y1),x,0);d:=B^2-4*A*C;if A&lt;&gt;1 then print(`\320\224\320\270\321\201\320\272\321\200\320\270\320\274\320\270\320\275\320\260\320\275\321\202:    `*D=d,sqrt(D)=sqrt(d));x1:=(-B-sqrt(d))/2/A;x2:=(-B+sqrt(d))/2/A;print(`\320\232\320\276\321\200\320\275\320\270:`); else print(`\320\232\320\276\321\200\320\275\320\270 \320\275\320\260\320\271\320\264\321\221\320\274 \320\277\321\200\320\270 \320\277\320\276\320\274\320\276\321\211\320\270 \321\202\320\265\320\276\321\200\320\265\320\274\321\213 \320\222\320\270\320\265\321\202\320\260:`);S:=solve(Y1);x1:=op(1,[S]);x2:=op(2,[S]); fi;print(x[1]=x1,x[2]=x2);y1:=(a*x1+c2)/b;y2:=(a*x2+c2)/b;print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276:  `*y[1]=y1,y[2]=y2);print(`\320\237\320\265\321\200\320\265\321\205\320\276\320\264\321\213 \320\261\321\213\320\273\320\270 \321\202\320\276\320\266\320\264\320\265\321\201\321\202\320\262\320\265\320\275\320\275\321\213\320\274\320\270.`);print(`\320\236\320\242\320\222\320\225\320\242:`);print(piecewise(x=x1,``,y=y1,``),piecewise(x=x2,``,y=y2,``));end:</MapleCode></EC-Button></Text-field>
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<Text-field style="Text" layout="Normal"><Font foreground="[0,0,1]">Find</Font>  <Font italic="true">x + y</Font> , <Font foreground="[0,0,1]">if  </Font> <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>  .</Text-field>
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action="click-event-handler">mapler:=proc(k1,a1,b1,k2,a2,b2) local Y,Y1,Y2,S1,S2,eq1,eq2;print(`\320\241\321\203\320\274\320\274\320\260 (\321\201 \320\277\320\276\320\273\320\276\320\266\320\270\321\202\320\265\320\273\321\214\320\275\321\213\320\274\320\270 \320\272\320\276\321\215\321\204\321\204\320\270\321\206\320\270\320\265\320\275\321\202\320\260\320\274\320\270)`);print(` \320\274\320\276\320\264\321\203\320\273\320\265\320\271 \320\262\321\201\320\265\320\263\320\264\320\260 \320\275\320\265\320\276\321\202\321\200\320\270\321\206\320\260\321\202\320\265\320\273\321\214\320\275\320\260.`);print(`\320\237\320\276\321\215\321\202\320\276\320\274\321\203 \320\264\320\260\320\275\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265`);Y1:=a1*x+b1*y;Y2:=a2*x+b2;Y:=k1*abs(Y1)+k2*abs(Y2)=0;print(%);print(`\320\261\321\203\320\264\320\265\321\202 \320\262\320\265\321\200\320\275\321\213\320\274 \321\200\320\260\320\262\320\265\320\275\321\201\321\202\320\262\320\276\320\274 \321\202\320\276\320\273\321\214\320\272\320\276 \320\277\321\200\320\270 \321\203\321\201\320\273\320\276\320\262\320\270\320\270`);print(piecewise(Y1=0,``,Y2=0,``));print(`\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 - \321\202\321\200\320\270\320\262\320\270\320\260\320\273\321\214\320\275\320\276:`);eq1:=x=-b2/a2;eq2:=y=a1*b2/a2/b1;print(piecewise(eq1,``,eq2,``));S1:=solve(eq1);S2:=solve(eq2);print(`\320\236\320\242\320\222\320\225\320\242:  `*x+y=S1+S2);end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart;mapler:=proc(k1,a1,b1,k2,a2,b2) local Y,Y1,Y2,S1,S2,eq1,eq2;print(`\320\230\320\267 \320\276\320\277\321\200\320\265\320\264\320\265\320\273\320\265\320\275\320\270\321\217 \320\260\320\261\321\201\320\276\320\273\321\216\321\202\320\275\320\276\320\271 \320\262\320\265\320\273\320\270\321\207\320\270\320\275\321\213 \321\201\320\273\320\265\320\264\321\203\320\265\321\202,`);print(`\321\207\321\202\320\276 \320\264\320\260\320\275\320\275\320\276\320\265 \321\200\320\260\320\262\320\265\320\275\321\201\321\202\320\262\320\276`);Y1:=a1*x+b1*y;Y2:=a2*x+b2;Y:=k1*abs(Y1)=-k2*abs(Y2);print(%);print(`\320\261\321\203\320\264\320\265\321\202 \320\262\320\265\321\200\320\275\321\213\320\274 \321\202\320\276\320\273\321\214\320\272\320\276 \320\277\321\200\320\270 \321\203\321\201\320\273\320\276\320\262\320\270\320\270`);print(piecewise(Y1=0,``,Y2=0,``));print(`\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 - \321\202\321\200\320\270\320\262\320\270\320\260\320\273\321\214\320\275\320\276:`);eq1:=x=-b2/a2;eq2:=y=a1*b2/a2/b1;print(piecewise(eq1,``,eq2,``));S1:=solve(eq1);S2:=solve(eq2);print(`\320\236\320\242\320\222\320\225\320\242:  `*x-y=S1-S2);end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,A1,a2,b2,c2,A2) local Y1,Y2,U,U1,U2,V1,V2,P1,P2,eq11,eq12,eq21,eq22,eq111,eq222;print(`\320\222 \320\270\321\201\321\205\320\276\320\264\320\275\320\276\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\320\265`);Y1:=a1*(x^2+y^2)+b1*(x+y)+c1*x*y=A1;Y2:=a2*(x^2+y^2)+b2*(x+y)+c2*x*y=A2;print(piecewise(Y1,``,Y2,``));print(`\320\267\320\260\320\274\320\265\320\275\320\270\320\274 \320\277\320\265\321\200\320\265\320\274\320\265\320\275\320\275\321\213\320\265 \320\277\320\276 \320\277\321\200\320\260\320\262\320\270\320\273\321\203:`);print(x+y=u,x*y=v);print(`\320\222\321\213\320\264\320\265\320\273\320\270\320\262 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\321\213 \321\201\321\203\320\274\320\274\321\213, \320\270\320\274\320\265\320\265\320\274:`);Y1:=subs({x^2=u^2-2*v-y^2,x=u-y,x*y=v},Y1);Y2:=subs({x^2=u^2-2*v-y^2,x=u-y,x*y=v},Y2);print(piecewise(Y1,``,Y2,``));print(`\320\222\321\213\321\200\320\260\320\267\320\270\320\274, \320\275\320\260\320\277\321\200\320\270\320\274\320\265\321\200, v \321\207\320\265\321\200\320\265\320\267 u:`);Y1:=v=solve(Y1,v);Y2:=subs({x^2=u^2-2*v-y^2,x=u-y,x*y=v},lhs(Y2))-A2=0;print(piecewise(Y1,``,Y2,``));print(`\320\235\320\270\320\266\320\275\320\265\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265, \320\277\320\276\321\201\320\273\320\265 \320\277\320\276\320\264\321\201\321\202\320\260\320\275\320\276\320\262\320\272\320\270, \320\277\320\276\320\267\320\262\320\276\320\273\320\270\321\202 \320\276\320\277\321\200\320\265\320\264\320\265\320\273\320\270\321\202\321\214 u:`);Y2:=sort(subs(Y1,lhs(Y2)))=0;print(%);if denom(coeff(lhs(Y2),u,2))&lt;&gt;1 then Y2:=sort(lhs(Y2)*denom(coeff(lhs(Y2),u,2)))=0;print(%); else  fi;U:=[solve(Y2)];U1:=op(1,U);U2:=op(2,U);print(u[1]=U1,u[2]=U2);V1:=subs(u=U1,rhs(Y1));V2:=subs(u=U2,rhs(Y1));print(`\320\241\320\273\320\265\320\264\320\276\320\262\320\260\321\202\320\265\320\273\321\214\320\275\320\276`);print(v[1]=V1,v[2]=V2);print(`\320\237\321\200\320\265\320\264\321\201\321\202\320\276\320\270\321\202 \321\200\320\265\321\210\320\270\321\202\321\214 \321\203\320\266\320\265 \320\264\320\262\320\265 \320\277\321\200\320\276\321\201\321\202\321\213\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);eq11:=x+y=U1;eq12:=x*y=V1;eq111:=({eq11,eq12});eq21:=x+y=U2;eq22:=x*y=V2;eq222:=({eq21,eq22});print(piecewise(eq11,``,eq12,``),piecewise(eq21,``,eq22,``));print(`\320\230\321\201\320\277\320\276\320\273\321\214\320\267\321\203\320\265\320\274 \321\202\320\276\321\202 \320\266\320\265 \320\274\320\265\321\202\320\276\320\264 \320\277\320\276\320\264\321\201\321\202\320\260\320\275\320\276\320\262\320\272\320\270.`);print(`\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \320\277\320\265\321\200\320\262\320\276\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);eq11:=y=U1-x;eq12:=x*(U1-x)-V1=0;print({eq11,eq12});eq11:=y=U1-x;eq12:=sort(x^2-U1*x+V1)=0;print({eq11,eq12});if U1^2-4*V1&gt;=0 then P1:=solve(eq111);print(P1);else P1:=0;print(`\320\224\320\265\320\271\321\201\321\202\320\262\320\270\321\202\320\265\320\273\321\214\320\275\321\213\321\205 \320\272\320\276\321\200\320\275\320\265\320\271 \320\275\320\265\321\202`);fi;print(`\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \320\262\321\202\320\276\321\200\320\276\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);eq21:=y=U2-x;eq22:=x*(U2-x)-V2=0;print({eq21,eq22});eq21:=y=U2-x;eq22:=sort(x^2-U2*x+V2)=0;print({eq21,eq22});if U2^2-4*V2&gt;=0 then P2:=solve(eq222);print(P2);else P2:=0; print(`\320\224\320\265\320\271\321\201\321\202\320\262\320\270\321\202\320\265\320\273\321\214\320\275\321\213\321\205 \320\272\320\276\321\200\320\275\320\265\320\271 \320\275\320\265\321\202`);fi;print(`\320\236\320\242\320\222\320\225\320\242:`);if P1&lt;&gt;0 and P2&lt;&gt;0 then print(P1,P2); else if P1=0 then print(P2) else print(P1); fi;fi;with(plots):implicitplot({a1*(x^2+y^2)+b1*(x+y)+c1*x*y=A1,a2*(x^2+y^2)+b2*(x+y)+c2*x*y=A2},x=-10..10,y=-10..10,thickness=2,numpoints=2000,color=green);end:</MapleCode></EC-Button></Text-field>
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<Text-field style="Text" layout="Normal">For what values of the parameters  <Font encoding="UTF-8" italic="true">\320\260 </Font> and  <Font italic="true">b</Font>  the system <Equation executable="false" style="2D Math" input-equation="" 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  has infinitely many solutions, and the point  <Equation executable="false" style="2D Math" input-equation="" 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 - one of them?</Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,a2,b2,c2,x1,y1) local Eq1,Eq2,eq1,eq2,B,eq10,eq20,A,eq0,Y;Eq1:=a1*x+b1*y=c1;Eq2:=a2*x+b2*y=c2;print(piecewise(Eq1,``,Eq2,``));print(`\320\232\320\276\321\215\321\204\321\204\320\270\321\206\320\270\320\265\320\275\321\202\321\213 \320\262 \320\273\320\270\320\275\320\265\320\271\320\275\321\213\321\205 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\321\217\321\205 \321\201\320\270\321\201\321\202\320\265\320\274\321\213`);print(`\320\264\320\276\320\273\320\266\320\275\321\213 \320\261\321\213\321\202\321\214 \320\277\321\200\320\276\320\277\320\276\321\200\321\206\320\270\320\276\320\275\320\260\320\273\321\214\320\275\321\213.`);eq1:=a1/a2=b1/b2;eq2:=a1/a2=c1/c2;B:=solve(eq1,b);eq10:=b=B;eq20:=a1*c2=c1*a2;eq20:=subs(b=B,eq20)/a;print(piecewise(eq1,``,eq2,``),piecewise(eq10,``,eq20,``));A:=solve(eq20,a);B:=subs(a=A,B);print(a=A,`   `*b=B);eq0:=subs({a=A,b=B},Eq1);print(%);Y:=solve(eq0,y);print(`\320\223\320\265\320\276\320\274\320\265\321\202\321\200\320\270\321\207\320\265\321\201\320\272\320\270\320\271 \320\276\320\261\321\200\320\260\320\267 \320\276\320\261\320\276\320\270\321\205 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271`);print(`\320\270\321\201\321\205\320\276\320\264\320\275\320\276\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 - \320\277\321\200\321\217\320\274\320\260\321\217`);print(y=Y);print(`\320\237\320\276\320\264\321\201\321\202\320\260\320\262\320\270\320\274 \320\272\320\276\320\276\321\200\320\264\320\270\320\275\320\260\321\202\321\213 \320\264\320\260\320\275\320\275\320\276\320\271 \321\202\320\276\321\207\320\272\320\270  `*M(x1,y1));print(`\320\262 \320\277\320\276\320\273\321\203\321\207\320\265\320\275\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\277\321\200\321\217\320\274\320\276\320\271:`);if y1=subs(x=x1,Y) then print(subs({x=x1,y=y1},y=Y));print(`\320\232\320\276\320\276\321\200\320\264\320\270\320\275\320\260\321\202\321\213 \321\202\320\276\321\207\320\272\320\270 M - \320\276\320\264\320\275\320\276 \320\270\320\267 \321\200\320\265\321\210\320\265\320\275\320\270\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213.`);print(`\320\236\320\242\320\222\320\225\320\242:  `*a=A,`   `*b=B); else print(subs({x=x1,y=y1},y&lt;&gt;Y));print(`\320\236\320\242\320\222\320\225\320\242:  \320\243 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 \320\261\320\265\321\201\320\272\320\276\320\275\320\265\321\207\320\275\320\276\320\265 \320\274\320\275\320\276\320\266\320\265\321\201\321\202\320\262\320\276`);print(`\321\200\320\265\321\210\320\265\320\275\320\270\320\271 \320\277\321\200\320\270  `*a=A,`   `*b=B,` \320\275\320\276 \321\202\320\276\321\207\320\272\320\260 `*M(x1,y1));print(`\320\235\320\225 \320\277\321\200\320\270\320\275\320\260\320\264\320\273\320\265\320\266\320\270\321\202 \321\215\321\202\320\276\320\274\321\203 \320\274\320\275\320\276\320\266\320\265\321\201\321\202\320\262\321\203.`); fi;end:</MapleCode></EC-Button></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" foreground="[128,0,0]">08</Font></Text-field>
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<Text-field style="Text" layout="Normal">For what values of the parameters  <Font encoding="UTF-8" italic="true">\320\260</Font>  and  <Font italic="true">b</Font>  the system <Equation executable="false" style="2D Math" input-equation="" 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 <Font foreground="[0,0,1]">has a unique solution - a point</Font><Equation executable="false" style="2D Math" input-equation="" 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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,a2,b2,c2,x1,x2) local Y1,Y2,A,B,eq01,eq02,eq03,eq1,Y11,eq2,Y22;print(`\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213`);Y1:=a1*x+b1*y=c1;Y2:=a2*x+b2*y=c2;print(piecewise(Y1,``,Y2,``));print(`\320\276\320\261\320\273\320\265\320\263\321\207\320\265\320\275\320\276 \321\202\320\265\320\274, \321\207\321\202\320\276 \320\270\320\267\320\262\320\265\321\201\321\202\320\275\320\276 \320\265\321\221 \321\207\320\260\321\201\321\202\320\275\320\276\320\265 \321\200\320\265\321\210\320\265\320\275\320\270\320\265 - \321\202\320\276\321\207\320\272\320\260`);print(M(x1,x2));eq01:=subs({x=x1,y=x2},Y1);eq02:=subs({x=x1,y=x2},Y2);print(`\320\237\320\276\320\264\321\201\321\202\320\260\320\275\320\276\320\262\320\272\320\260 \320\272\320\276\320\276\321\200\320\264\320\270\320\275\320\260\321\202 \321\215\321\202\320\276\320\271 \321\202\320\276\321\207\320\272\320\270 \320\277\321\200\320\270\320\262\320\265\320\264\321\221\321\202 \321\201\320\270\321\201\321\202\320\265\320\274\321\203 \320\272 \320\273\320\270\320\275\320\265\320\271\320\275\320\276\320\274\321\203 \320\262\320\270\320\264\321\203: `);print(piecewise(eq01,``,eq02,``));print(`\320\240\320\265\321\210\320\260\320\265\320\274 \320\274\320\265\321\202\320\276\320\264\320\276\320\274 \320\277\320\276\320\264\321\201\321\202\320\260\320\275\320\276\320\262\320\272\320\270:`);eq01:=b=solve(eq01,b);eq02:=b=solve(eq02,b);print(piecewise(eq01,``,eq02,``));eq03:=rhs(eq01)=rhs(eq02);eq03:=lhs(eq03)-rhs(eq03)=0;print(eq01,eq03);eq03:=a=solve(eq03,a);A:=rhs(eq03);B:=subs(a=A,solve(eq01,b));print(`\320\230\321\202\320\260\320\272  `*a=A,`   `*b=B);print(`\320\222 \321\215\321\202\320\276\320\274 \321\201\320\273\321\203\321\207\320\260\320\265  \321\201\320\270\321\201\321\202\320\265\320\274a \320\261\321\203\320\264\320\265\321\202 \320\270\320\274\320\265\321\202\321\214 \320\262\320\270\320\264:`);eq1:=subs({a=A,b=B},Y1);Y11:=solve(eq1,y);eq1:=y=Y11;eq2:=subs({a=A,b=B},Y2);Y22:=solve(eq2,y);eq2:=y=Y22;print(piecewise(eq1,``,eq2,``));print(`\320\223\321\200\320\260\321\204\320\270\321\207\320\265\321\201\320\272\320\260\321\217 \320\277\321\200\320\276\320\262\320\265\321\200\320\272\320\260:`);with(plots):implicitplot({eq1,eq2},x=-10..10,y=-10..10,thickness=2,color=green);print(%);print(`\320\236\320\242\320\222\320\225\320\242:`*a=A,b=B);end:</MapleCode></EC-Button></Text-field>
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<Text-field style="Text" layout="Normal">For what values of the parameters  <Font encoding="UTF-8" italic="true">\320\260</Font>  and  <Font italic="true">b</Font>  the system <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>  <Font foreground="[0,0,1]">has a unique solution - 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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,a2,b2,c2,x1,x2) local Y1,Y2,A,B,A1,A2,B1,B2,eq1,eq2,eq3,eq11,eq110,eq22,eq220,F,G,eq01,eq02,eq03;print(`\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213`);Y1:=a1*x+b1*y=c1;Y2:=a2*x+b2*y=c2;print(piecewise(Y1,``,Y2,``));print(`\320\276\320\261\320\273\320\265\320\263\321\207\320\265\320\275\320\276 \321\202\320\265\320\274, \321\207\321\202\320\276 \320\270\320\267\320\262\320\265\321\201\321\202\320\275\320\276 \320\265\321\221 \321\207\320\260\321\201\321\202\320\275\320\276\320\265 \321\200\320\265\321\210\320\265\320\275\320\270\320\265 - \321\202\320\276\321\207\320\272\320\260`);print(M(x1,x2));eq01:=subs({x=x1,y=x2},Y1);eq02:=subs({x=x1,y=x2},Y2);print(`\320\237\320\276\320\264\321\201\321\202\320\260\320\275\320\276\320\262\320\272\320\260 \320\272\320\276\320\276\321\200\320\264\320\270\320\275\320\260\321\202 \321\215\321\202\320\276\320\271 \321\202\320\276\321\207\320\272\320\270 \320\277\321\200\320\270\320\262\320\265\320\264\321\221\321\202 \321\201\320\270\321\201\321\202\320\265\320\274\321\203 \320\272 \320\277\321\200\320\276\321\201\321\202\320\276\320\274\321\203 \320\262\320\270\320\264\321\203: `);print(piecewise(eq01,``,eq02,``));print(`\320\240\320\265\321\210\320\260\320\265\320\274 \320\274\320\265\321\202\320\276\320\264\320\276\320\274 \320\277\320\276\320\264\321\201\321\202\320\260\320\275\320\276\320\262\320\272\320\270:`);B:=solve(eq02,b);eq02:=b=B;eq01:=subs(b=B,eq01);A:=solve(eq01,a);print({eq01,eq02});eq01:=lhs(eq01)-rhs(eq01)=0;print(%);eq01:=factor(lhs(eq01))=0;print(%);A1:=op(1,[A]);A2:=op(2,[A]);print(a[1]=A1,a[2]=A2);B1:=subs(a=A1,B);B2:=subs(a=A2,B);print(b[1]=B1,b[2]=B2);print(`\320\222 \321\201\320\273\321\203\321\207\320\260\320\265`,{a[1]=A1,b[1]=B1});print(`  \321\201\320\270\321\201\321\202\320\265\320\274a \320\261\321\203\320\264\320\265\321\202 \320\270\320\274\320\265\321\202\321\214 \320\262\320\270\320\264:`);eq1:=subs({a=A1,b=B1},Y1);eq2:=subs({a=A1,b=B1},Y2);print(piecewise(eq1,``,eq2,``));eq3:={eq1,eq2};print(`\320\270 \321\202\320\276\320\273\321\214\320\272\320\276 \320\277\320\260\321\200\320\260 \320\272\320\276\320\276\321\200\320\264\320\270\320\275\320\260\321\202 \321\202\320\276\321\207\320\272\320\270 \320\234 - \321\200\320\265\321\210\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213.`);solve(eq3,{x,y});print(%);print(`\320\225\321\201\320\273\320\270 \320\266\320\265`,{a[2]=A2,b[2]=B2});eq11:=subs({a=A2,b=B2},Y1);eq22:=subs({a=A2,b=B2},Y2);eq110:=(lhs(eq11)-rhs(eq11))/coeff(lhs(eq11),x,1)=0;eq220:=(lhs(eq22)-rhs(eq22))/coeff(lhs(eq22),x,1)=0;if lhs(eq110)&lt;&gt;lhs(eq220) then print(piecewise(eq11,``,eq22,``));print(piecewise(eq110,``,eq220,``));print(`\320\255\321\202\320\276 - \320\262\321\202\320\276\321\200\320\276\320\265 \321\200\320\265\321\210\320\265\320\275\320\270\320\265`);print(`\320\236\320\242\320\222\320\225\320\242:`);print({a=A1,b=B1},{a=A2,b=B2}); else print(` \321\202\320\276 \320\272\320\260\320\266\320\264\320\276\320\265 \320\270\320\267 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271  \320\277\321\200\320\270\320\275\320\270\320\274\320\260\320\265\321\202 \320\276\320\264\320\270\320\275\320\260\320\272\320\276\320\262\321\213\320\271 \320\262\320\270\320\264:`); print(eq110);print(`\320\255\321\202\320\276 \321\201\320\273\321\203\321\207\320\260\320\271 \320\261\320\265\321\201\320\272\320\276\320\275\320\265\321\207\320\275\320\276\320\263\320\276 \320\274\320\275\320\276\320\266\320\265\321\201\321\202\320\262\320\260 \321\200\320\265\321\210\320\265\320\275\320\270\320\271, \321\207\321\202\320\276 \320\275\320\260\321\201 \320\275\320\265 \321\203\321\201\321\202\321\200\320\260\320\270\320\262\320\260\320\265\321\202. `);print(`\320\236\320\242\320\222\320\225\320\242:`);print(a=A1,b=B1);fi;with(plots):F:=implicitplot({eq1,eq2},x=-10..10,y=-10..10,thickness=2,color=green):G:=implicitplot({eq22,eq11},x=-10..10,y=-10..10,thickness=2,color=red):display({F,G});print(%);end:</MapleCode></EC-Button></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KVEnbWFwbGVyRicvJSVzaXplR1EjMTBGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRK1swLDg1LDEyOV1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGPS1JKG1mZW5jZWRHRiQ2Ji1GIzY/LUYsNiVRImFGJy9GNkY0L0Y8USdpdGFsaWNGJy1JI21vR0YkNi1RIl5GJy9GPFEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR0Zbby1JI21uR0YkNiRRIjJGJ0ZPLUZMNi1RIixGJ0ZPRlEvRlRGNEZVRldGWUZlbkZnbi9Gam5RJjAuMGVtRicvRl1vUSwwLjMzMzMzMzNlbUYnLUZMNi1RKiZ1bWludXMwO0YnRk9GUUZTRlVGV0ZZRmVuRmduL0ZqblEsMC4yMjIyMjIyZW1GJy9GXW9GXnBGRUZiby1GX282JFEiMUYnRk9Gam9GRUZiby1GLDYlUSJiRidGSEZJRmJvLUZfbzYkUSIzRidGT0Zqb0Zeby1GTDYtUSIqRidGT0ZRRlNGVUZXRllGZW5GZ24vRmpuUSwwLjE2NjY2NjdlbUYnL0Zdb0ZdcUZjcEZib0ZmcC1GTDYtUSIrRidGT0ZRRlNGVUZXRllGZW5GZ25GXXBGX3BGRUZib0ZgcEZib0ZgcEYvL0Y5US5bMTkyLDE5MiwxOTJdRidGT0YvRmJxRk8tRiw2I1EhRidGL0Y4Rk8=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Hyperlink linktarget="Wks:07/09.mw" hyperlink="true"><HyperlinkImage height="25" width="25" zoomable="false" drawcaption="false" captionalignment="0" captionposition="1">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<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIkXSNGKi0lLkJPVU5EU19IRUlHSFRHRi8tJSlDSElMRFJFTkc2Ig==</Drawing-Root></HyperlinkImage></Hyperlink></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" foreground="[128,0,0]">10</Font></Text-field>
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<Text-field style="Text" layout="Normal">  The parameters <Font italic="true">a</Font>  and  <Font italic="true">b</Font>  are such that a pair of numbers   <Equation executable="false" style="2D Math" input-equation="" 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  and  <Equation executable="false" style="2D Math" input-equation="" 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 <Font foreground="[0,0,1]">is one of the solutions  of the the system</Font>  <Equation executable="false" style="2D Math" input-equation="" 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 . <Font foreground="[0,0,1]">Find more at least one other such pair.</Font></Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,a2,b2,c2,x0,y0) local X,Y,eq01,eq02,A0,B0,C0,d,A11,A1,A2,B11,B1,B2,C11,C1,C2,n1,n2,eq3,A,B,eq1,eq2,eq4,S,y1,y2,x1,x2;print(`\320\224\320\260\320\275\320\275\320\260\321\217 \320\277\320\260\321\200\320\260 \321\207\320\270\321\201\320\265\320\273:  `*x[0]=x0,`    `*y[0]=y0);print(`\320\237\320\276\321\201\320\273\320\265 \320\277\320\276\320\264\321\201\321\202\320\260\320\275\320\276\320\262\320\272\320\270 \320\262 \321\201\320\270\321\201\321\202\320\265\320\274\321\203`);eq01:=a1*x+b1*y=c1;eq02:=a2*x^2+b2*y^2=c2;print(piecewise(eq01,``,eq02,``));print(`\320\264\320\260\320\275\320\275\321\213\321\205 \320\267\320\275\320\260\321\207\320\265\320\275\320\270\320\271 \320\265\321\221 \320\272\320\276\321\200\320\275\320\265\320\271, \320\277\320\276\320\273\321\203\321\207\320\270\320\274 \321\201\320\270\321\201\321\202\320\265\320\274\321\203`);print(`\320\270\320\267 \320\273\320\270\320\275\320\265\320\271\320\275\321\213\321\205 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271 \320\276\321\202\320\275\320\276\321\201\320\270\321\202\320\265\320\273\321\214\320\275\320\276 \320\277\320\260\321\200\320\260\320\274\320\265\321\202\321\200\320\276\320\262:`);eq1:=subs({x=x0,y=y0},lhs(eq01))=c1;eq2:=subs({x=x0,y=y0},lhs(eq02))=c2;print(piecewise(eq1,``,eq2,``));print(`\320\237\320\276\321\201\320\273\320\265 \320\276\321\207\320\265\320\262\320\270\320\264\320\275\321\213\321\205 \321\203\320\277\321\200\320\276\321\211\320\265\320\275\320\270\320\271:`);A1:=coeff(lhs(eq1),a,1);A2:=coeff(lhs(eq2),a,1);B1:=coeff(lhs(eq1),b,1);B2:=coeff(lhs(eq2),b,1);n1:=ilcm(denom(A1),denom(B1),denom(c1));n2:=ilcm(denom(A2),denom(B2),denom(c2));A1:=A1*n1;B1:=B1*n1;C1:=c1*n1;A2:=A2*n2;B2:=B2*n2;C2:=c2*n2;eq1:=A1*a+B1*b=C1;eq2:=A2*a+B2*b=C2;print(piecewise(eq1,``,eq2,``));print(`\320\222\321\213\321\200\320\260\320\267\320\270\320\274 \320\277\320\260\321\200\320\260\320\274\320\265\321\202\321\200  \320\260  \321\207\320\265\321\200\320\265\320\267 b:`);eq1:=a=solve(eq1,a);eq2:=a=solve(eq2,a);print(piecewise(eq1,``,eq2,``));eq3:=solve(eq1,a)-solve(eq2,a)=0;print(%);B:=solve(eq3,b);A:=subs(b=B,solve(eq1,a));print(`\320\230\321\201\320\272\320\276\320\274\321\213\320\265 \320\272\320\276\321\200\320\275\320\270:   `*a=A,b=B);A1:=subs({a=A,b=B},a1);B1:=subs({a=A,b=B},b1);C1:=subs({a=A,b=B},c1);A2:=subs({a=A,b=B},a2);B2:=subs({a=A,b=B},b2);C2:=subs({a=A,b=B},c2);eq1:=A1*x+B1*y=C1;eq2:=A2*x^2+B2*y^2=C2;print(`\320\222 \321\215\321\202\320\276\320\274 \321\201\320\273\321\203\321\207\320\260\320\265 \320\262\320\270\320\264 \320\270\321\201\321\205\320\276\320\264\320\275\320\276\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);print(piecewise(eq1,``,eq2,``));n1:=ilcm(denom(A1),denom(B1),denom(C1));n2:=ilcm(denom(A2),denom(B2),denom(C2));if n1&lt;&gt;1 or n2&lt;&gt;1 then A1:=A1*n1;B1:=B1*n1;C1:=C1*n1;A2:=A2*n2;B2:=B2*n2;C2:=C2*n2;eq1:=A1*x+B1*y=C1;eq2:=A2*x^2+B2*y^2=C2;print(`\320\235\320\265\320\274\320\275\320\276\320\263\320\276 \321\203\320\277\321\200\320\276\321\201\321\202\320\270\320\274:`);print(piecewise(eq1,``,eq2,``));else fi;print(`\320\222\321\213\321\200\320\260\320\267\320\270\320\274  \321\205  \321\207\320\265\321\200\320\265\320\267  \321\203 ...`);X:=solve(eq1,x);print(x=X);eq3:=subs(x=X,lhs(eq2))=C2;print(%);eq3:=expand(lhs(eq3))-C2=0;eq4:=eq3;print(%);A11:=coeff(lhs(eq3),y,2);B11:=coeff(lhs(eq3),y,1);C11:=coeff(lhs(eq3),y,0);n1:=ilcm(denom(A11),denom(B11),denom(C11));n2:=igcd(numer(A11),numer(B11),numer(C11));A11:=A11*n1/n2;B11:=B11*n1/n2;C11:=C11*n1/n2;eq3:=A11*y^2+B11*y+C11=0;if A11&lt;0 then eq3:=-lhs(eq3)=0;else fi;if lhs(eq3)&lt;&gt;lhs(eq4) then print(eq3) else fi;A0:=coeff(lhs(eq3),y,2);B0:=coeff(lhs(eq3),y,1);C0:=coeff(lhs(eq3),y,0);d:=B0^2-4*A0*C0;if C0&lt;&gt;0 then print(`\320\224\320\270\321\201\320\272\321\200\320\270\320\274\320\270\320\275\320\260\320\275\321\202:   `*D=d,sqrt(D)=sqrt(d));else fi;S:=solve(eq3);y1:=op(1,[S]);y2:=op(2,[S]);print(y[1]=y1,y[2]=y2);x1:=subs(y=y1,X);x2:=subs(y=y2,X);print({x[1]=x1,y[1]=y1},{x[2]=x2,y[2]=y2});print(`\320\240\320\265\320\267\321\203\320\273\321\214\321\202\320\260\321\202 \321\202\320\276\320\266\320\264\320\265\321\201\321\202\320\262\320\265\320\275\320\275\321\213\321\205 \320\277\321\200\320\265\320\276\320\261\321\200\320\260\320\267\320\276\320\262\320\260\320\275\320\270\320\271 - \320\275\320\276\320\262\320\276\320\265 \321\200\320\265\321\210\320\265\320\275\320\270\320\265:`);if x1=x0 then print({x[2]=x2,y[2]=y2}); else print({x[1]=x1,y[1]=y1});fi;end:</MapleCode></EC-Button></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Hyperlink linktarget="Wks:07/10.mw" hyperlink="true"><HyperlinkImage height="25" width="25" zoomable="false" drawcaption="false" captionalignment="0" captionposition="1">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<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIkXSNGKi0lLkJPVU5EU19IRUlHSFRHRi8tJSlDSElMRFJFTkc2Ig==</Drawing-Root></HyperlinkImage></Hyperlink></Text-field>
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<Text-field style="Text" layout="Normal">For what values of the parameter <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMV1GJy8lMGZvbnRfc3R5bGVfbmFtZUdRMkNoYXJhY3RlclN0eWxlNzAxRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y2USVUZXh0RicvRjlRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMV1GJy8lMGZvbnRfc3R5bGVfbmFtZUdRMkNoYXJhY3RlclN0eWxlNzAxRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y2USVUZXh0RicvRjlRJ25vcm1hbEYn</Equation>  the roots  <Equation executable="false" style="Text" input-equation="" 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 <Font foreground="[0,0,1]">satisfy the relation</Font> <Equation executable="false" style="Text" input-equation="" 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action="click-event-handler">restart: mapler:=proc(A,B,C,k,b,alpha) local Y,eq1,eq2,eq3,eqq,eq01,eq02,X1,X2,F,U,V,eq,A1,B1,C1,Z1,Z2,n,N,d;print(x[2]=k*x[1]+b);print(`\320\237\321\200\320\265\320\264\320\277\320\276\320\273\320\276\320\266\320\270\320\274. \321\207\321\202\320\276 \320\264\320\260\320\275\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265`);Y:=A*x^2+B*x+C=0;print(%);print(`\320\270\320\274\320\265\320\265\321\202 \320\272\320\276\321\200\320\275\320\270:    `*x[1]=u,x[2]=v);eq1:=u+v=-B/A;eq2:=u*v=C/A;eq3:=v=k*u+b;print(`\320\237\321\200\320\270\320\274\320\265\320\275\320\270\320\274 \321\202\320\265\320\276\321\200\320\265\320\274\321\203 \320\222\320\270\320\265\321\202\320\260 \320\270 \320\277\320\276\320\273\321\203\321\207\320\270\320\274 \321\201\320\270\321\201\321\202\320\265\320\274\321\203 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271:`);F:=piecewise(eq1,``,eq2,``,eq3,``);print(F);print(`\320\230\320\267 \320\277\320\265\321\200\320\262\320\276\320\263\320\276 \320\270 \321\202\321\200\320\265\321\202\321\214\320\265\320\263\320\276 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265\320\271 \321\201\320\273\320\265\320\264\321\203\320\265\321\202:`);eq1:=u=-B/A-k*u-b;print(%);U:=-(B/A+b)/(1+k);eq1:=u=U;print(%);V:=subs(u=rhs(eq1),rhs(eq3));print(`\320\241\320\270\321\201\321\202\320\265\320\274\320\260 \320\277\321\200\320\270\320\276\320\261\321\200\320\265\321\202\320\260\320\265\321\202 \320\262\320\270\320\264:`);eq3:=v=V;print(piecewise(eq1,``,eq2,``,eq3,``));print(`\320\237\320\276\320\264\321\201\321\202\320\260\320\262\320\270\320\274 \321\202\320\265\320\277\320\265\321\200\321\214  u  \320\270  v  \320\262\320\276 \320\262\321\202\320\276\321\200\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265:`);eq2:=U*V=C/A;print(%);eq2:=expand(U*V)=C/A;eq:=lhs(eq2)-rhs(eq2)=0;A1:=coeff(lhs(eq),alpha,2);B1:=coeff(lhs(eq),alpha,1);C1:=coeff(lhs(eq),alpha,0);if A1&lt;0 then A1:=-A1;B1:=-B1;C1:=-C1;else fi;eq:=A1*alpha^2+B1*alpha+C1=0;print(eq);n:=igcd(numer(A1),numer(B1),numer(C1));N:=ilcm(denom(A1),denom(B1),denom(C1));A1:=A1*N/n;B1:=B1*N/n;C1:=C1*N/n;eqq:=A1*alpha^2+B1*alpha+C1=0;if lhs(eqq)&lt;&gt;lhs(eq) then print(eqq) else fi;print(`\320\240\320\265\321\210\320\270\320\274 \320\277\320\276\320\273\321\203\321\207\320\265\320\275\320\275\320\276\320\265 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265.`);d:=B1^2-4*A1*C1;Z1:=(-B1-sqrt(d))/2/A1;Z2:=(-B1+sqrt(d))/2/A1;if d=0 then print(alpha=Z1);eq01:=subs(alpha=Z1,Y);print(%);X1:=subs(alpha=Z1,U);X2:=subs(alpha=Z1,V);print(x[1]=X1,x[2]=X2);else if B1&lt;&gt;0 then print(`\320\225\320\263\320\276 \320\264\320\270\321\201\320\272\321\200\320\270\320\274\320\270\320\275\320\260\320\275\321\202:   `*D=d,sqrt(D)=sqrt(d));else fi;print(`\320\232\320\276\321\200\320\275\320\270:   `*alpha[1]=Z1,alpha[2]=Z2);print(`\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \320\277\321\200\320\276\320\262\320\265\321\200\320\270\320\274 \320\275\320\265\320\277\320\276\321\201\321\200\320\265\320\264\321\201\321\202\320\262\320\265\320\275\320\275\320\276\320\271 \320\277\320\276\320\264\321\201\321\202\320\260\320\275\320\276\320\262\320\272\320\276\320\271.`);print(`\320\222 \321\201\320\273\321\203\321\207\320\260\320\265     `*alpha=Z1);print(`\320\270\321\201\321\205\320\276\320\264\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\277\321\200\320\270\320\275\320\270\320\274\320\260\320\265\321\202 \320\262\320\270\320\264:`);eq01:=subs(alpha=Z1,Y);print(%);X1:=subs(alpha=Z1,U);X2:=subs(alpha=Z1,V);print(x[1]=X1,x[2]=X2);print(`\320\222\320\276 \320\262\321\202\320\276\321\200\320\276\320\274 \321\201\320\273\321\203\321\207\320\260\320\265, \320\272\320\276\320\263\320\264\320\260     `*alpha[2]=Z2);eq02:=subs(alpha=Z2,Y);print(%);X1:=subs(alpha=Z2,U);X2:=subs(alpha=Z2,V);print(x[1]=X1,x[2]=X2); fi;print(`\320\233\320\265\320\263\320\272\320\276 \320\262\320\270\320\264\320\265\321\202\321\214, \321\207\321\202\320\276 \320\277\320\276\321\201\321\202\320\276\321\200\320\276\320\275\320\275\320\270\321\205 \321\200\320\265\321\210\320\265\320\275\320\270\320\271 \320\275\320\265\321\202.`);if d&lt;&gt;0 then print(`\320\236\320\242\320\222\320\225\320\242:  `*alpha[1]=Z1,alpha[2]=Z2);else print(`\320\236\320\242\320\222\320\225\320\242:  `*alpha=Z1);fi end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart: mapler:=proc(A,B,C,s,alpha) local Y,eq1,eq2,eq3,eq11,eq12,F,d,U1,U2,U3,U4,U5,V1,V2,S,S1,S2,K,Z1,Z2,R1,R2;print(`\320\237\321\200\320\265\320\264\320\277\320\276\320\273\320\276\320\266\320\270\320\274. \321\207\321\202\320\276 \320\264\320\260\320\275\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265`);Y:=A*x^2+B*x+C=0;print(%);print(`\320\270\320\274\320\265\320\265\321\202 \320\272\320\276\321\200\320\275\320\270:    `*x[1]=u,x[2]=v);eq1:=u+v=-B/A;eq2:=u*v=C/A;eq3:=v=u^s;print(`\320\237\321\200\320\270\320\274\320\265\320\275\320\270\320\274 \321\202\320\265\320\276\321\200\320\265\320\274\321\203 \320\222\320\270\320\265\321\202\320\260 \320\270 \320\277\320\276\320\273\321\203\321\207\320\270\320\274 \321\201\320\270\321\201\321\202\320\265\320\274\321\203 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271:`);F:=piecewise(eq1,``,eq2,``,eq3,``);print(F);if s=2 then print(`\320\230\320\267 \320\277\320\265\321\200\320\262\320\276\320\263\320\276 \320\270 \321\202\321\200\320\265\321\202\321\214\320\265\320\263\320\276 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265\320\271 \321\201\320\273\320\265\320\264\321\203\320\265\321\202:`);eq1:=u+u^s=-B/A;print(%);eq1:=u^s+u+B/A=0;print(%);print(`\320\240\320\265\321\210\320\270\320\274 \320\277\320\276\320\273\321\203\321\207\320\265\320\275\320\275\320\276\320\265 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265.`);d:=1-4*B/A;print(`\320\225\320\263\320\276 \320\264\320\270\321\201\320\272\321\200\320\270\320\274\320\270\320\275\320\260\320\275\321\202:   `*D=d);U1:=(-1-sqrt(d))/2;U2:=(-1+sqrt(d))/2;print(u[1]=U1,u[2]=U2);V1:=U1^s;V2:=U2^s;print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276:  `*v[1]=V1,v[2]=V2);print(`\320\236\321\201\321\202\320\260\320\273\320\276\321\201\321\214 \320\276\320\277\321\200\320\265\320\264\320\265\320\273\320\270\321\202\321\214 \321\201\320\260\320\274 \320\277\320\260\321\200\320\260\320\274\320\265\321\202\321\200.`);if coeff(lhs(Y),alpha,2)=0 then S:=solve(eq2,alpha);Z1:=subs({u=U1,v=V1},S);Z2:=subs({u=U2,v=V2},S); print(`\320\233\320\265\320\263\320\272\320\276 \320\262\320\270\320\264\320\265\321\202\321\214, \321\207\321\202\320\276 \320\277\320\276\321\201\321\202\320\276\321\200\320\276\320\275\320\275\320\270\321\205 \321\200\320\265\321\210\320\265\320\275\320\270\320\271 \320\275\320\265\321\202.`); print(`\320\236\320\242\320\222\320\225\320\242:  `*alpha[1]=Z1,alpha[2]=Z2);else print(`\320\232\320\276\321\200\320\275\320\270 \320\262 \320\275\320\260\321\210\320\265\320\274 \321\201\320\273\321\203\321\207\320\260\320\265 \320\264\320\276\320\273\320\266\320\275\321\213 \320\261\321\213\321\202\321\214 \320\276\320\264\320\275\320\276\320\263\320\276 \320\267\320\275\320\260\320\272\320\260.`);print(`\320\237\320\276\320\264\321\205\320\276\320\264\320\270\321\202 \321\202\320\276\320\273\321\214\320\272\320\276 \320\277\320\260\321\200\320\260    `*u[2],v[2]);print(`\320\222 \321\215\321\202\320\276\320\274 \321\201\320\273\321\203\321\207\320\260\320\265 \320\262\321\202\320\276\321\200\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 \320\264\320\260\321\221\321\202:`);S:=solve(eq2,alpha^2);Z1:=subs({u=U1,v=V1},S);Z2:=subs({u=U2,v=V2},S);if Z1&gt;0 then print(alpha[1]=-sqrt(Z1),alpha[2]=sqrt(Z1));else print(`\320\236\320\242\320\222\320\225\320\242:   `*alpha[1]=-sqrt(Z2),alpha[2]=sqrt(Z2)); fi fi;else print(`\320\230\320\267 \320\262\321\202\320\276\321\200\320\276\320\263\320\276 \320\270 \321\202\321\200\320\265\321\202\321\214\320\265\320\263\320\276 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271 \320\270\320\274\320\265\320\265\320\274:`);eq2:=u^4=C/A;print(%);S:=solve(eq2,a^2);K:=coeff(S,u,4);S1:=-sqrt(K)*u^2;S2:=sqrt(K)*u^2;print(alpha[1]=S1,alpha[2]=S2);print(`\320\237\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\200\320\260\321\201\320\277\320\260\320\273\320\276\321\201\321\214 \320\275\320\260 \320\264\320\262\320\260:`);eq11:=u+u^3+subs(alpha=S1,B/A)=0;eq12:=u+u^3+subs(alpha=S2,B/A)=0;print(eq11,eq12);print(`\320\237\320\276\320\264\321\205\320\276\320\264\320\270\321\202 \320\270 \321\202\321\200\320\270\320\262\320\270\320\260\320\273\321\214\320\275\321\213\320\271 \320\272\320\276\321\200\320\265\320\275\321\214:`);U1:=0;print(u[1]=0);print(`\320\235\320\260\320\271\320\264\321\221\320\274 \320\276\321\201\321\202\320\260\320\273\321\214\320\275\321\213\320\265 \320\272\320\276\321\200\320\275\320\270:`);eq11:=factor(lhs(eq11)/u)=0;eq12:=factor(lhs(eq12)/u)=0;print(eq11,eq12);R1:=solve(eq11,u);R2:=solve(eq12,u);U2:=op(1,[R1]);U3:=op(2,[R1]);U4:=op(1,[R2]);U5:=op(2,[R2]);print(u[2]=U2,u[3]=U3,u[4]=U4,u[5]=U5);print(v[1]=0,v[2]=U2^3,v[3]=U3^3,v[4]=U4^3,v[5]=U5^3);print(`\320\236\320\242\320\222\320\225\320\242:`);print(alpha[1]=0,alpha[2]=-sqrt(K)*U2^2,alpha[3]=sqrt(K)*U2^2,alpha[4]=-sqrt(K)*U3^2,alpha[5]=sqrt(K)*U3^2);fi  end:</MapleCode></EC-Button></Text-field>
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<Text-field style="Text" layout="Normal">Find all the real values of the parameter <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMV1GJy8lMGZvbnRfc3R5bGVfbmFtZUdRMkNoYXJhY3RlclN0eWxlNTM5RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y2USVUZXh0RicvRjlRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMV1GJy8lMGZvbnRfc3R5bGVfbmFtZUdRMkNoYXJhY3RlclN0eWxlNTM5RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y2USVUZXh0RicvRjlRJ25vcm1hbEYn</Equation>  , for which one of the roots  of the the equation <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>  <Font foreground="[0,0,1]">is the cube of the other.</Font></Text-field>
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action="click-event-handler">restart: mapler:=proc(A,B,C,s,alpha) local Y,eq1,eq2,eq3,eq11,eq12,F,d,U1,U2,U3,U4,U5,V1,V2,S,S1,S2,K,Z1,Z2,R1,R2;print(`\320\237\321\200\320\265\320\264\320\277\320\276\320\273\320\276\320\266\320\270\320\274. \321\207\321\202\320\276 \320\264\320\260\320\275\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265`);Y:=A*x^2+B*x+C=0;print(%);print(`\320\270\320\274\320\265\320\265\321\202 \320\272\320\276\321\200\320\275\320\270:    `*x[1]=u,x[2]=v);eq1:=u+v=-B/A;eq2:=u*v=C/A;eq3:=v=u^s;print(`\320\237\321\200\320\270\320\274\320\265\320\275\320\270\320\274 \321\202\320\265\320\276\321\200\320\265\320\274\321\203 \320\222\320\270\320\265\321\202\320\260 \320\270 \320\277\320\276\320\273\321\203\321\207\320\270\320\274 \321\201\320\270\321\201\321\202\320\265\320\274\321\203 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271:`);F:=piecewise(eq1,``,eq2,``,eq3,``);print(F);if s=2 then print(`\320\230\320\267 \320\277\320\265\321\200\320\262\320\276\320\263\320\276 \320\270 \321\202\321\200\320\265\321\202\321\214\320\265\320\263\320\276 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265\320\271 \321\201\320\273\320\265\320\264\321\203\320\265\321\202:`);eq1:=u+u^s=-B/A;print(%);eq1:=u^s+u+B/A=0;print(%);print(`\320\240\320\265\321\210\320\270\320\274 \320\277\320\276\320\273\321\203\321\207\320\265\320\275\320\275\320\276\320\265 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265.`);d:=1-4*B/A;print(`\320\225\320\263\320\276 \320\264\320\270\321\201\320\272\321\200\320\270\320\274\320\270\320\275\320\260\320\275\321\202:   `*D=d);U1:=(-1-sqrt(d))/2;U2:=(-1+sqrt(d))/2;print(u[1]=U1,u[2]=U2);V1:=U1^s;V2:=U2^s;print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276:  `*v[1]=V1,v[2]=V2);print(`\320\236\321\201\321\202\320\260\320\273\320\276\321\201\321\214 \320\276\320\277\321\200\320\265\320\264\320\265\320\273\320\270\321\202\321\214 \321\201\320\260\320\274 \320\277\320\260\321\200\320\260\320\274\320\265\321\202\321\200.`);if coeff(lhs(Y),alpha,2)=0 then S:=solve(eq2,alpha);Z1:=subs({u=U1,v=V1},S);Z2:=subs({u=U2,v=V2},S); print(`\320\233\320\265\320\263\320\272\320\276 \320\262\320\270\320\264\320\265\321\202\321\214, \321\207\321\202\320\276 \320\277\320\276\321\201\321\202\320\276\321\200\320\276\320\275\320\275\320\270\321\205 \321\200\320\265\321\210\320\265\320\275\320\270\320\271 \320\275\320\265\321\202.`); print(`\320\236\320\242\320\222\320\225\320\242:  `*alpha[1]=Z1,alpha[2]=Z2);else print(`\320\232\320\276\321\200\320\275\320\270 \320\262 \320\275\320\260\321\210\320\265\320\274 \321\201\320\273\321\203\321\207\320\260\320\265 \320\264\320\276\320\273\320\266\320\275\321\213 \320\261\321\213\321\202\321\214 \320\276\320\264\320\275\320\276\320\263\320\276 \320\267\320\275\320\260\320\272\320\260.`);print(`\320\237\320\276\320\264\321\205\320\276\320\264\320\270\321\202 \321\202\320\276\320\273\321\214\320\272\320\276 \320\277\320\260\321\200\320\260    `*u[2],v[2]);print(`\320\222 \321\215\321\202\320\276\320\274 \321\201\320\273\321\203\321\207\320\260\320\265 \320\262\321\202\320\276\321\200\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 \320\264\320\260\321\221\321\202:`);S:=solve(eq2,alpha^2);Z1:=subs({u=U1,v=V1},S);Z2:=subs({u=U2,v=V2},S);if Z1&gt;0 then print(alpha[1]=-sqrt(Z1),alpha[2]=sqrt(Z1));else print(`\320\236\320\242\320\222\320\225\320\242:   `*alpha[1]=-sqrt(Z2),alpha[2]=sqrt(Z2)); fi fi;else print(`\320\230\320\267 \320\262\321\202\320\276\321\200\320\276\320\263\320\276 \320\270 \321\202\321\200\320\265\321\202\321\214\320\265\320\263\320\276 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271 \320\270\320\274\320\265\320\265\320\274:`);eq2:=u^4=C/A;print(%);S:=solve(eq2,a^2);K:=coeff(S,u,4);S1:=-sqrt(K)*u^2;S2:=sqrt(K)*u^2;print(alpha[1]=S1,alpha[2]=S2);print(`\320\237\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\200\320\260\321\201\320\277\320\260\320\273\320\276\321\201\321\214 \320\275\320\260 \320\264\320\262\320\260:`);eq11:=u+u^3+subs(alpha=S1,B/A)=0;eq12:=u+u^3+subs(alpha=S2,B/A)=0;print(eq11,eq12);print(`\320\237\320\276\320\264\321\205\320\276\320\264\320\270\321\202 \320\270 \321\202\321\200\320\270\320\262\320\270\320\260\320\273\321\214\320\275\321\213\320\271 \320\272\320\276\321\200\320\265\320\275\321\214:`);U1:=0;print(u[1]=0);print(`\320\235\320\260\320\271\320\264\321\221\320\274 \320\276\321\201\321\202\320\260\320\273\321\214\320\275\321\213\320\265 \320\272\320\276\321\200\320\275\320\270:`);eq11:=factor(lhs(eq11)/u)=0;eq12:=factor(lhs(eq12)/u)=0;print(eq11,eq12);R1:=solve(eq11,u);R2:=solve(eq12,u);U2:=op(1,[R1]);U3:=op(2,[R1]);U4:=op(1,[R2]);U5:=op(2,[R2]);print(u[2]=U2,u[3]=U3,u[4]=U4,u[5]=U5);print(v[1]=0,v[2]=U2^3,v[3]=U3^3,v[4]=U4^3,v[5]=U5^3);print(`\320\236\320\242\320\222\320\225\320\242:`);print(alpha[1]=0,alpha[2]=-sqrt(K)*U2^2,alpha[3]=sqrt(K)*U2^2,alpha[4]=-sqrt(K)*U3^2,alpha[5]=sqrt(K)*U3^2);fi  end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,a2,b2,c2) local eq1,eq2,eq20,X,Y,eq3,eq4;print(`\320\236\320\264\320\275\320\276 \320\270\320\267 \321\200\320\265\321\210\320\265\320\275\320\270\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 `);eq1:=a1*x+b1*y=c1*x*y;eq2:=a2*x+b2*y=c2*x*y;print(piecewise(eq1,``,eq2,``));print(`\320\276\321\207\320\265\320\262\320\270\320\264\320\275\320\276:  `*x[0]=0,`   `*y[0]=0);eq2:=(a1*x+b1*y)/(a2*x+b2*y)=c1/c2;eq20:=(a1*x+b1*y)*c2=(a2*x+b2*y)*c1;Y:=solve(eq20,y);eq3:=y=Y;print(`\320\240\320\260\320\267\320\264\320\265\320\273\320\270\320\274 \320\277\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\275\320\260 \320\262\321\202\320\276\321\200\320\276\320\265:`);print([eq2]*`=&gt;`*[eq20]);eq4:=subs(y=Y,eq1);print([eq3]*`=&gt;`*[eq4]);eq4:=eq4/x;X:=solve(eq4,x);Y:=subs(x=X,Y);print(`\320\235\320\260\321\210\320\273\320\270 \320\270 \320\275\320\265\321\202\321\200\320\270\320\262\320\270\320\260\320\273\321\214\320\275\320\276\320\265 \321\200\320\265\321\210\320\265\320\275\320\270\320\265:`);print(x[1]=X,`  `*y[1]=Y);print(`\320\236\320\242\320\222\320\225\320\242:  `*{x=0,`   `*y=0},`   `*{x=X,`   `*y=Y});end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,a2,b2,c2) local eq1,eq2,X,Y,eq11,eq21,x1,y1,s,s1;eq1:=a1*x^2+b1*y^2=c1;eq2:=a2*x^2+b2*y^2=c2;print(piecewise(eq1,``,eq2,``));print(`\320\240\320\265\321\210\320\265\320\275\320\270\320\265 \320\264\320\260\320\275\320\275\320\276\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 \320\276\321\207\320\265\320\262\320\270\320\264\320\275\320\276:`);X:=solve(eq1,x^2);eq11:=x^2=X;Y:=solve(eq2,y^2);eq21:=y^2=subs(x^2=X,Y);print(piecewise(eq11,``,eq21,``));Y:=solve(eq21,y^2);X:=subs(y^2=Y,X);eq11:=x^2=X;eq21:=y^2=Y;print(piecewise(eq11,``,eq21,``));x1:=sqrt(X);y1:=sqrt(Y);print(`\320\232\320\276\320\276\321\200\320\264\320\270\320\275\320\260\321\202\321\213 \320\262\320\265\321\200\321\210\320\270\320\275 \320\277\321\200\321\217\320\274\320\276\321\203\320\263\320\276\320\273\321\214\320\275\320\270\320\272\320\260:`);print(A(-x1,-y1),`   `*B(-x1,y1),`   `*C(x1,y1),`   `*'D'(x1,-y1));s:=sqrt(m^2+n^2);s1:=subs({m=x[A]-x[C],n=y[A]-y[C]},s);print(`\320\230\321\201\320\272\320\276\320\274\320\260\321\217 \320\262\320\265\320\273\320\270\321\207\320\270\320\275\320\260 - \321\203\320\264\320\262\320\276\320\265\320\275\320\275\320\260\321\217 \320\264\320\273\320\270\320\275\320\260 \320\264\320\270\320\260\320\263\320\276\320\275\320\260\320\273\320\270 \320\220\320\241:`);print(S=2*s1,`   `*S=4*sqrt(x^2+y^2));print(`\320\236\320\242\320\222\320\225\320\242:  `*S=4*sqrt(X+Y));end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3) local Y,eq,eq1,eq2,eq3,eq4,eq5,eq11,eq12,eq13,eq21,eq22,eq23,A,B,C,n,N,d,X1,X2,Y1,Y2,Z1,Z2,Z;eq1:=a1*x*y+b1*x+c1*y=d1;eq2:=a2*y*z+b2*y+c2*z=d2;eq3:=a3*x*z+b3*x+c3*z=d3;Y:=piecewise(eq1,``,eq2,``,eq3,``);print(%);print(`\320\222\321\213\320\275\320\265\321\201\320\265\320\274 \320\267\320\260 \321\201\320\272\320\276\320\261\320\272\320\270  \321\203  \320\262 \320\273\320\265\320\262\320\276\320\271 \321\207\320\260\321\201\321\202\320\270`);print(`\320\272\320\260\320\266\320\264\320\276\320\263\320\276 \320\270\320\267 \320\277\320\265\321\200\320\262\321\213\321\205 \320\264\320\262\321\203\321\205 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);eq:={eq1,eq2,eq3};eq1:=y*(a1*x+c1)=d1-b1*x;eq2:=y*(a2*z+b2)=d2-c2*z;print(piecewise(eq1,``,eq2,``,eq3,``));print(`\320\240\320\260\320\267\320\264\320\265\320\273\320\270\320\274 \320\277\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\275\320\260 \320\262\321\202\320\276\321\200\320\276\320\265:`);eq4:=lhs(eq1)/lhs(eq2)=rhs(eq1)/rhs(eq2);print(%);print(`\320\255\321\202\320\276 \320\277\321\200\320\265\320\276\320\261\321\200\320\260\320\267\320\276\320\262\320\260\320\275\320\270\320\265 \321\202\320\276\320\266\320\264\320\265\321\201\321\202\320\262\320\265\320\275\320\275\320\276, \320\265\321\201\320\273\320\270`);print(y&lt;&gt;0,z&lt;&gt;-b2/a2,z&lt;&gt;d2/c2);print(`\320\237\320\276\321\201\320\273\320\265\320\264\320\275\320\265\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\277\321\200\320\270\320\262\320\265\320\264\321\221\320\274 \320\272 \321\200\320\260\321\206\320\270\320\276\320\275\320\260\320\273\321\214\320\275\320\276\320\274\321\203 \320\262\320\270\320\264\321\203:`);eq4:=(a1*x+c1)*(d2-c2*z)=(d1-b1*x)*(a2*z+b2);print(%);eq4:=sort(expand(lhs(eq4)))=sort(expand(rhs(eq4)));print(%);eq4:=lhs(eq4)-rhs(eq4)=0;print(%);print(`\320\222\321\213\321\200\320\260\320\267\320\270\320\274, \320\275\320\260\320\277\321\200\320\270\320\274\320\265\321\200,  z  \321\207\320\265\321\200\320\265\320\267  \321\205:`);Z:=solve(eq4,z);print(z=Z);print(`\320\270 \320\277\320\276\320\264\321\201\321\202\320\260\320\262\320\270\320\274 \321\200\320\265\320\267\321\203\320\273\321\214\321\202\320\260\321\202 \320\262 \321\202\321\200\320\265\321\202\321\214\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);eq5:=subs(z=Z,eq3);print(%);eq5:=expand(lhs(eq5))-rhs(eq5)=0;print(%);A:=coeff(lhs(eq5),x,2);B:=coeff(lhs(eq5),x,1);C:=coeff(lhs(eq5),x,0);n:=igcd(numer(A),numer(B),numer(C));N:=ilcm(denom(A),denom(B),denom(C));A:=A*N/n;B:=B*N/n;C:=C*N/n;print(`\320\232\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\277\321\200\320\270\320\276\320\261\321\200\320\265\320\273\320\276 \320\277\321\200\320\276\321\201\321\202\320\276\320\271 \320\262\320\270\320\264:`);eq5:=A*x^2+B*x+C=0;print(%);d:=B^2-4*A*C;print(`\320\224\320\270\321\201\320\272\321\200\320\270\320\274\320\270\320\275\320\260\320\275\321\202:    `*D=d);X1:=(-B-sqrt(d))/2/A;X2:=(-B+sqrt(d))/2/A;print(`\320\232\320\276\321\200\320\275\320\270:   `*x[1]=X1,x[2]=X2);Z1:=subs(x=X1,Z);Z2:=subs(x=X2,Z);print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276,    `*z[1]=Z1,z[2]=Z2);Y:=(d1-b1*x)/(a1*x+c1);print(`\320\237\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 \320\264\320\260\321\221\321\202:    `*y=Y);Y1:=subs(x=X1,Y);Y2:=subs(x=X2,Y);print(`\320\236\321\202\320\272\321\203\320\264\320\260:    `*y[1]=Y1,y[2]=Y2);eq11:=x=X1;eq12:=y=Y1;eq13:=z=Z1;eq21:=x=X2;eq22:=y=Y2;eq23:=z=Z2;print(`\320\237\320\265\321\200\320\265\321\205\320\276\320\264\321\213 \320\261\321\213\320\273\320\270 \321\202\320\276\320\266\320\264\320\265\321\201\321\202\320\262\320\265\320\275\320\275\321\213\320\274\320\270.   \320\236\320\242\320\222\320\225\320\242:`);print(piecewise(eq11,``,eq12,``,eq13,``),piecewise(eq21,``,eq22,``,eq23,``));end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3) local Y,eq,eq1,eq2,eq3,eq4,eq5,eq11,eq12,eq13,eq21,eq22,eq31,eq23,A,B,C,n,N,d,X1,X2,Y1,Y2,Z1,Z2,Z;print(`\320\224\320\260\320\275\320\275\321\203\321\216 \321\201\320\270\321\201\321\202\320\265\320\274\321\203`);eq1:=a1*x*y+b1*x+c1*y=d1;eq2:=a2*y*z+b2*y+c2*z=d2;eq3:=a3*x*z+b3*x+c3*z=d3;eq11:=x*y=solve(eq1,x*y);eq21:=y*z=solve(eq2,y*z);eq31:=x*z=solve(eq3,x*z);Y:=piecewise(eq11,``,eq21,``,eq31,``);print(%);Y:=piecewise(eq1,``,eq2,``,eq3,``);eq:={eq1,eq2,eq3};eq1:=y*(a1*x+c1)=d1-b1*x;eq2:=y*(a2*z+b2)=d2-c2*z;print(`\320\267\320\260\320\274\320\265\320\275\320\270\320\274 \320\275\320\260 \321\202\320\276\320\266\320\264\320\265\321\201\321\202\320\262\320\265\320\275\320\275\321\203\321\216 \320\265\320\271:`);print(piecewise(eq1,``,eq2,``,eq3,``));print(`\320\240\320\260\320\267\320\264\320\265\320\273\320\270\320\274 \320\277\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\275\320\260 \320\262\321\202\320\276\321\200\320\276\320\265:`);eq4:=lhs(eq1)/lhs(eq2)=rhs(eq1)/rhs(eq2);print(%);print(`\320\255\321\202\320\276 \320\277\321\200\320\265\320\276\320\261\321\200\320\260\320\267\320\276\320\262\320\260\320\275\320\270\320\265 \321\202\320\276\320\266\320\264\320\265\321\201\321\202\320\262\320\265\320\275\320\275\320\276, \320\265\321\201\320\273\320\270`);print(y&lt;&gt;0,z&lt;&gt;-b2/a2,z&lt;&gt;d2/c2);print(`\320\237\320\276\321\201\320\273\320\265\320\264\320\275\320\265\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\277\321\200\320\270\320\262\320\265\320\264\321\221\320\274 \320\272 \321\200\320\260\321\206\320\270\320\276\320\275\320\260\320\273\321\214\320\275\320\276\320\274\321\203 \320\262\320\270\320\264\321\203:`);eq4:=(a1*x+c1)*(d2-c2*z)=(d1-b1*x)*(a2*z+b2);print(%);eq4:=sort(expand(lhs(eq4)))=sort(expand(rhs(eq4)));print(%);eq4:=lhs(eq4)-rhs(eq4)=0;print(%);print(`\320\222\321\213\321\200\320\260\320\267\320\270\320\274, \320\275\320\260\320\277\321\200\320\270\320\274\320\265\321\200,  z  \321\207\320\265\321\200\320\265\320\267  \321\205:`);Z:=solve(eq4,z);print(z=Z);print(`\320\270 \320\277\320\276\320\264\321\201\321\202\320\260\320\262\320\270\320\274 \321\200\320\265\320\267\321\203\320\273\321\214\321\202\320\260\321\202 \320\262 \321\202\321\200\320\265\321\202\321\214\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);eq5:=subs(z=Z,eq3);print(%);eq5:=expand(lhs(eq5))-rhs(eq5)=0;print(%);A:=coeff(lhs(eq5),x,2);B:=coeff(lhs(eq5),x,1);C:=coeff(lhs(eq5),x,0);n:=igcd(numer(A),numer(B),numer(C));N:=ilcm(denom(A),denom(B),denom(C));A:=A*N/n;B:=B*N/n;C:=C*N/n;print(`\320\232\320\262\320\260\320\264\321\200\320\260\321\202\320\275\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\277\321\200\320\270\320\276\320\261\321\200\320\265\320\273\320\276 \320\277\321\200\320\276\321\201\321\202\320\276\320\271 \320\262\320\270\320\264:`);eq5:=A*x^2+B*x+C=0;print(%);d:=B^2-4*A*C;print(`\320\224\320\270\321\201\320\272\321\200\320\270\320\274\320\270\320\275\320\260\320\275\321\202:    `*D=d);X1:=(-B-sqrt(d))/2/A;X2:=(-B+sqrt(d))/2/A;print(`\320\232\320\276\321\200\320\275\320\270:   `*x[1]=X1,x[2]=X2);Z1:=subs(x=X1,Z);Z2:=subs(x=X2,Z);print(`\320\241\320\276\320\276\321\202\320\262\320\265\321\202\321\201\321\202\320\262\320\265\320\275\320\275\320\276,    `*z[1]=Z1,z[2]=Z2);Y:=(d1-b1*x)/(a1*x+c1);print(`\320\237\320\265\321\200\320\262\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \321\201\320\270\321\201\321\202\320\265\320\274\321\213 \320\264\320\260\321\221\321\202:    `*y=Y);Y1:=subs(x=X1,Y);Y2:=subs(x=X2,Y);print(`\320\236\321\202\320\272\321\203\320\264\320\260:    `*y[1]=Y1,y[2]=Y2);eq11:=x=X1;eq12:=y=Y1;eq13:=z=Z1;eq21:=x=X2;eq22:=y=Y2;eq23:=z=Z2;print(`\320\237\320\265\321\200\320\265\321\205\320\276\320\264\321\213 \320\261\321\213\320\273\320\270 \321\202\320\276\320\266\320\264\320\265\321\201\321\202\320\262\320\265\320\275\320\275\321\213\320\274\320\270.   \320\236\320\242\320\222\320\225\320\242:`);print(piecewise(eq11,``,eq12,``,eq13,``),piecewise(eq21,``,eq22,``,eq23,``));end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3) local X,Y,Z,eq1,eq2,eq3,Y1,Y2,Y3,eq;Y1:=a1*x^2+b1*y+c1*z=d1;Y2:=a2*x+b2*y^2+c2*z=d2;Y3:=a3*x+b3*y+c3*z^2=d3;Y:=piecewise(Y1,``,Y2,``,Y3,``);print(%);print(`\320\241\320\276\321\201\321\202\320\260\320\262\320\270\320\274 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265-\321\201\321\203\320\274\320\274\321\203 \320\262\321\201\320\265\321\205 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\271 \321\201\320\270\321\201\321\202\320\265\320\274\321\213:`);eq:=sort(Y1+Y2+Y3);print(%);print(`\320\233\320\265\320\263\320\272\320\276 \320\262\321\213\320\264\320\265\320\273\320\270\321\202\321\214 \320\277\320\276\320\273\320\275\321\213\320\265 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\321\213:`);X:=-coeff(lhs(eq),x,1)/2/coeff(lhs(eq),x,2);Y:=-coeff(lhs(eq),y,1)/2/coeff(lhs(eq),y,2);Z:=-coeff(lhs(eq),z,1)/2/coeff(lhs(eq),z,2);with(student):eq:=completesquare(eq,x);eq:=completesquare(eq,y);eq:=completesquare(eq,z);print(%);eq:=sort(lhs(eq)-d1-d2-d3)=0;print(%);print(`\320\241\321\203\320\274\320\274\320\260 \320\272\320\262\320\260\320\264\321\200\320\260\321\202\320\276\320\262 \320\261\321\203\320\264\320\265\321\202 \320\275\321\203\320\273\321\221\320\274 \321\202\320\276\320\273\321\214\320\272\320\276 \320\262 \321\202\321\200\320\270\320\262\320\270\320\260\320\273\321\214\320\275\320\276\320\274 \321\201\320\273\321\203\321\207\320\260\320\265:`);eq1:=x=X;eq2:=y=Y;eq3:=z=Z;print(piecewise(eq1,``,eq2,``,eq3,``));print(`\320\237\321\200\320\276\320\262\320\265\321\200\320\270\320\274, \321\201\321\202\320\260\320\275\320\265\321\202 \320\273\320\270 \320\272\320\260\320\266\320\264\320\276\320\265 \321\203\321\200\320\260\320\262\320\275\320\265\320\275\320\270\320\265 \320\262\320\265\321\200\320\275\321\213\320\274 \321\200\320\260\320\262\320\265\320\275\321\201\321\202\320\262\320\276\320\274:`);Y1:=subs({x=X,y=Y,z=Z},Y1);Y2:=subs({x=X,y=Y,z=Z},Y2);Y3:=subs({x=X,y=Y,z=Z},Y3);print(Y1,Y2,Y3);if lhs(Y1)=d1 then print(`\320\236\320\242\320\222\320\225\320\242:`);print(piecewise(eq1,``,eq2,``,eq3,``)); else print(`\320\236\320\242\320\222\320\225\320\242:   \321\200\320\265\321\210\320\265\320\275\320\270\320\271 \320\275\320\265\321\202.`) fi end:</MapleCode></EC-Button></Text-field>
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action="click-event-handler">restart: mapler:=proc(a1,b1,a2,b2,a,b) local x1,x2,x3,x4,y1,y2,y3,y4,X,X1,X2,Y1,Y2,Y,eq1,eq2,eq01,eq21,eq11,n1,n2,n01,n02,n11,n12,n21,n22,m01,m02,eq02,eq12,eq22,y01,y02,eq011,eq012,eq022,eq021,G1,G2,T;print(`\303\202\303\262\303\256\303\260\303\256\303\245 \303\263\303\260\303\240\303\242\303\255\303\245\303\255\303\250\303\245 \303\261\303\250\303\261\303\262\303\245\303\254\303\273`);eq1:=a1*abs(a*x+b)+b1*y=1;eq2:=a2*x+b2*abs(y)=0;Y:=piecewise(eq1,``,eq2,``);print(%);print(`\303\244\303\240\302\270\303\262 \303\242\303\256\303\247\303\254\303\256\303\246\303\255\303\256\303\261\303\262\303\274 \303\242\303\273\303\260\303\240\303\247\303\250\303\262\303\274  \303\265  \303\267\303\245\303\260\303\245\303\247  \303\263:`);X:=-b2/a2*abs(y);eq21:=x=X;eq11:=a1*abs(-a*b2*abs(y)/a2+b)+b1*y=1;Y:=piecewise(eq11,``,eq21,``);print(%);print(`\303\217\303\256\303\261\303\253\303\245 \303\257\303\256\303\244\303\261\303\262\303\240\303\255\303\256\303\242\303\252\303\250,\303\257\303\245\303\260\303\242\303\256\303\245 \303\263\303\260\303\240\303\242\303\255\303\245\303\255\303\250\303\245 \303\261\303\250\303\261\303\262\303\245\303\254\303\273`);print(`\303\260\303\240\303\261\303\257\303\250\303\270\303\245\303\254 \303\252\303\240\303\252 \303\261\303\256\303\242\303\256\303\252\303\263\303\257\303\255\303\256\303\261\303\262\303\274:`);                                            eq01:=a1*abs(a*b2*y/a2+b)+b1*y=1;n1:=y&lt;0;  eq02:=a1*abs(-a*b2*y/a2+b)+b1*y=1;n2:=y&gt;=0;print(piecewise(eq01,n1,eq02,n2));print(`\303\200 \303\262\303\245\303\257\303\245\303\260\303\274 \303\263\303\241\303\245\303\260\302\270\303\254 \303\250 \303\257\303\256\303\261\303\253\303\245\303\244\303\255\303\250\303\251 \303\254\303\256\303\244\303\263\303\253\303\274.`);print(`\303\217\303\256\303\253\303\263\303\267\303\250\303\253\303\250 \303\261\303\256\303\242\303\256\303\252\303\263\303\257\303\255\303\256\303\261\303\262\303\274 \303\267\303\245\303\262\303\273\303\260\302\270\303\265 \303\263\303\260\303\240\303\242\303\255\303\245\303\255\303\250\303\251.`);print(`\303\210\303\265 \303\252\303\256\303\260\303\255\303\250 \303\244\303\256\303\253\303\246\303\255\303\273 \303\257\303\260\303\250\303\255\303\240\303\244\303\253\303\245\303\246\303\240\303\262\303\274 \303\263\303\252\303\240\303\247\303\273\303\242\303\240\303\245\303\254\303\273\303\254  \303\257\303\260\303\256\303\254\303\245\303\246\303\263\303\262\303\252\303\240\303\254.`); y01:=-b*a2/a/b2;y02:=b*a2/a/b2; if y01&lt;0 and y02&gt;0 then                                  eq011:=-a1*(a*b2*y/a2+b)+b1*y=1;y1:=solve(%);if a*b2/a2&gt;0 then n11:=y&lt;y01;else n01:=y&lt;0;n02:=y&gt;=y01;n11:={n01,n02}; fi;                                   eq012:=a1*(a*b2*y/a2+b)+b1*y=1;y2:=solve(%);if a*b2/a2&gt;0 then n01:=y&gt;=y01;n02:=y&lt;0;n12:={n01,n02};else fi;                 eq021:=-a1*(a*b2*y/a2-b)+b1*y=1;y3:=solve(%);if a*b2/a2&lt;0 then n21:=y&gt;=y02;else m01:=y&gt;=0;m02:=y&lt;=y02;n21:={m01,m02};fi;                               eq022:=a1*(a*b2*y/a2-b)+b1*y=1;y4:=solve(%);if a*b2/a2&lt;0 then m01:=y&gt;=0;m02:=y&lt;y2;n22:={m01,m02};else n22:=y&gt;=y02;fi;print(piecewise(n11,eq011,n12,eq012,n21,eq021,n22,eq022));print(y[1]=y1,y[2]=y2,y[3]=y3,y[4]=y4);print(`\303\217\303\256\303\244\303\256\303\270\303\253\303\250 \303\242\303\261\303\245 \303\267\303\245\303\262\303\273\303\260\303\245 \303\257\303\240\303\260\303\273 \303\252\303\256\303\260\303\245\303\255\303\251.`);x1:=simplify(subs(y=y1,X));x2:=simplify(subs(y=y2,X));x3:=simplify(subs(y=y3,X));x4:=simplify(subs(y=y4,X));if y1&lt;-b*a2/a/b2 then print({y=y1,x=x1});else fi;if y2&gt;=-b*a2/a/b2 and y2&lt;0 then print({y=y2,x=x2});else fi;if y3&lt;b*a2/a/b2 and y3&gt;=0 then print({y=y3,x=x3});else fi;if y4&gt;b*a2/a/b2 then print({y=y4,x=x4});else fi;Y1:=min(y1,y2,y3,y4);Y2:=max(y1,y2,y3,y4);X1:=min(x1,x2,x3,x4);X2:=max(x1,x2,x3,x4);print(`\303\235\303\262\303\256 \303\257\303\256\303\244\303\262\303\242\303\245\303\260\303\246\303\244\303\240\303\245\303\262 \303\250 \303\243\303\260\303\240\303\264\303\250\303\267\303\245\303\261\303\252\303\256\303\245 \303\260\303\245\303\270\303\245\303\255\303\250\303\245:`);with(plots):G1:=implicitplot(eq1,x=X1-1..X2+1,y=Y1-1..Y2+1,thickness=3,color=green,numpoints=2000):G2:=implicitplot(eq2,x=X1-1..X2+1,y=Y1-1..Y2+1,thickness=3,color=red,numpoints=2000):T:=textplot([[x1-0.2,y1-0.3,A(x1,y1)],[x2+0.3,y2-0.2,B(x2,y2)],[x3-0.2,y3+0.4,C(x3,y3)],[x4-0.3,y4-0.2,F(x4,y4)]],color=blue):display({G1,G2,T});else eq01:=-a1*(a*b2*y/a2+b)+b1*y=1;n1:=y&lt;0;eq02:=a1*(-a*b2*y/a2+b)+b1*y=1;n2:=y&gt;=0;print({eq01,n1});print({eq02,n2});y1:=solve(eq01);y2:=solve(eq02);print(y1,y2);x1:=simplify(subs(y=y1,X));x2:=simplify(subs(y=y2,X));X1:=min(x1,x2);X2:=max(x1,x2);Y1:=min(y1,y2);Y2:=max(y1,y2);with(plots):G1:=implicitplot(eq1,x=-10..10,y=Y1-1..Y2+1,thickness=3,color=green,numpoints=2000):G2:=implicitplot(eq2,x=X1-1..X2+1,y=Y1-1..Y2+1,thickness=3,color=red,numpoints=2000):T:=textplot([[0.2,y1-0.2,O(0,0)],[x2-0.2,y2-0.2,A(x2,y2)]],color=blue):display({G1,G2,T});   fi end;
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action="click-event-handler">restart: mapler:=proc(a1,b1,c1,d1,C1,a2,b2,c2,d2,C2) local eq1,eq2,eq01,eq02,eq03,C3,eq0,x0,y0,z0,t0;eq1:=a1*x+b1*y+c1*z+d1*t=C1;eq2:=sqrt(a2^2-a1^2*x^2)+sqrt(b2^2-b1^2*y^2)+sqrt(c2^2-c1^2*z^2)+sqrt(d2^2-d1^2*t^2)=C2;print(piecewise(eq1,``,eq2,``));print(a=(a1*x,sqrt(a2^2-a1^2*x^2)),b=(b1*y,sqrt(b2^2-b1^2*y^2)));print(c=(c1*z,sqrt(c2^2-c1^2*z^2)),d=(d1*t,sqrt(d2^2-d1^2*t^2)));print(abs(a)=a2,`   `*abs(b)=b2,`   `*abs(c)=c2,`   `*abs(d)=d2);print(`\320\241\320\232\320\220\320\233\320\257\320\240\320\235\320\253\320\231 \320\272\320\262\320\260\320\264\321\200\320\260\321\202 \320\262\320\265\320\272\321\202\320\276\321\200\320\276\320\262:`);print((a+b+c+d)^2=[C1]^2+[C2]^2);print(`\320\222\320\265\320\272\321\202\320\276\321\200\321\213 \320\272\320\276\320\273\320\273\320\270\320\275\320\265\320\260\321\200\320\275\321\213 \320\270 \321\201\320\276\320\275\320\260\320\277\321\200\320\260\320\262\320\273\320\265\320\275\321\213, \321\202.\320\272. \320\264\320\273\320\270\320\275\320\260 `);print(`\321\201\321\203\320\274\320\274\321\213 \320\262\320\265\320\272\321\202\320\276\321\200\320\276\320\262 \321\200\320\260\320\262\320\275\320\260 \321\201\321\203\320\274\320\274\320\265 \320\270\321\205 \320\264\320\273\320\270\320\275.`);print((sqrt(C1^2+C2^2))*`=`*abs(a)+abs(b)+abs(c)+abs(d)=abs(a+b+c+d));print(`\320\232\320\276\320\276\321\200\320\264\320\270\320\275\320\260\321\202\321\213 \321\202\320\260\320\272\320\270\321\205 \320\262\320\265\320\272\321\202\320\276\321\200\320\276\320\262 \320\277\321\200\320\276\320\277\320\276\321\200\321\206\320\270\320\276\320\275\320\260\320\273\321\214\320\275\321\213 \320\270\321\205 \320\264\320\273\320\270\320\275\320\260\320\274.`);print(`\320\236\321\200\320\264\320\270\320\275\320\260\321\202\321\213 \321\203 \320\275\320\270\321\205 \320\277\320\276\320\273\320\276\320\266\320\270\321\202\320\265\320\273\321\214\320\275\321\213 \320\270 \321\201\321\203\320\274\320\274\320\260  \320\260\320\261\321\201\321\206\320\270\321\201\321\201 \320\277\320\276\320\273\320\276\320\266\320\270\321\202\320\265\320\273\321\214\320\275\320\260.`);print(`\320\241\320\273\320\265\320\264\320\276\320\262\320\260\321\202\320\265\320\273\321\214\320\275\320\276 \320\260\320\261\321\201\321\206\320\270\321\201\321\201\321\213 \321\202\320\260\320\272\320\266\320\265 \320\277\320\276\320\273\320\276\320\266\320\270\321\202\320\265\320\273\321\214\320\275\321\213.`);print(`\320\222\321\213\321\200\320\260\320\266\320\260\320\265\320\274 \320\262\321\201\320\265 \320\277\320\265\321\200\320\265\320\274\320\265\320\275\320\275\321\213\320\265 \321\207\320\265\321\200\320\265\320\267   \321\205:`);eq01:=y=x*a1*b2/a2/b1;eq02:=z=x*a1*c2/c1/a2;eq03:=t=x*a1*d2/d1/a2;print(piecewise(eq1,``,eq01,``,eq02,``,eq03,``));C3:=a1+a1*b2/a2+a1*c2/a2+a1*d2/a2;eq0:=x*C3=C1;x0:=C1/C3;print(eq0,`    `*x=x0);y0:=x0*a1*b2/a2/b1;z0:=x0*a1*c2/c1*a2;t0:=x0*a1*d2/d1/a2;print(`\320\236\320\242\320\222\320\225\320\242:  `*x=x0,`   `*y=y0,`   `*z=z0,`   `*t=t0);print(`\320\237\320\240\320\236\320\222\320\225\320\240\320\232\320\220:`);print(subs({x=x0,y=y0,z=z0,t=t0},eq1),simplify(subs({x=x0,y=y0,z=z0,t=t0},eq2)));end:</MapleCode></EC-Button></Text-field>
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