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# Mapler. 05. ?lgebraic equations & Index

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Mapler :: 05 :: Rational ?lgebraic equations

1 :: The equivalence of equations

 ? Condition Activate Solution Variants 01 Solve the equation 02 Solve the equation 03 Find the distance between the root of the equation and the point 04 Find the distance between the root of the equation and the point 05 Find the distance between the root of the equation and the point 06 Find the distance between the root of the equation and the point 07 Find the distance between the root of the equation and the point

2 :: Vieta Theorem

 ? Condition Activate Solution Variants 08 Without solving the equation, find the ratio of the sum of the roots to the modulus of their difference 09 Without solving the equation, find the ratio of the product of the roots to the modulus of their difference 10 Without solving the equation to find the absolute difference of the squares of its roots 11 Without solving the equation to find the absolute difference of its roots

3 :: Rational equation of higher degree

 ? Condition Activate Solution Variants 12 Solve the equation 13 Solve the equation 14 Solve the equation 15 Solve the equation 16 Solve the equation 17 Solve the equation 18 Solve the equation 19 Solve the equation 20 Find the sum of the real roots of the equation 21 Find the sum of the real roots of the equation 22 Find the sum of the real roots of the equation 23 Solve the equation 24 Solve the equation 25 Solve the equation 26 Solve the equation 27 Solve the equation 28 Solve the equation 29 Solve the equation 30 Find the larger of the roots of the equation 31 Solve the equation 32 Solve the equation 33 Solve the equation

4 :: Equation with the module

 ? Condition Activate Solution Variants 34 Solve the equation 35 Solve the equation 36 Solve the equation 37 Solve the equation 38 Solve the equation 39 Solve the equation 40 Solve the equation 41 Solve the equation

5 :: Rational-fractional equation

 ? Condition Activate Solution Variants 42 Solve the equation 43 Solve the equation 44 Solve the equation 45 Solve the equation 46 Solve the equation 47 Solve the equation 48 Solve the equation 49 Solve the equation 50 Solve the equation 51 Solve the equation 52 Solve the equation 53 Solve the equation 54 Solve the equation 55 Solve the equation 56 Solve the equation 57 Solve the equation 58 Solve the equation

6 :: Equation with a parameter

 ? Condition Activate Solution Variants 59 Find for what value of the parameter a equation has equal roots 60 At any value of a quadratic polynomial has equal roots?