Mapler :: 05 :: Rational аlgebraic 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 :: Rationalfractional 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?





