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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?