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PinkJimsonTea
@PinkJimsonTea
July 2022
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определите число корней уравнения: а) -2х^2-4х+1=-2\х
как решить данное уравнение? графически?
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ShirokovP
Verified answer
ОДЗ:
x ≠ 0
- 2x^2 - 4x + 1 + 2/x = 0
- 2x^3 - 4x^2 + x + 2 = 0 // : (-1)
2x^3 + 4x^2 - x - 2 = 0
2x^2(x + 2) - 1(x + 2) = 0
(2x^2 - 1) (x + 2) = 0
x + 2 = 0 ==> x1 = - 2
2x^2 - 1 = 0 ==> x^2 = 1/2 ==> x2 = √2/2 ; x3 = - √2/2
Ответ:
3
2 votes
Thanks 1
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Answers & Comments
Verified answer
ОДЗ:x ≠ 0
- 2x^2 - 4x + 1 + 2/x = 0
- 2x^3 - 4x^2 + x + 2 = 0 // : (-1)
2x^3 + 4x^2 - x - 2 = 0
2x^2(x + 2) - 1(x + 2) = 0
(2x^2 - 1) (x + 2) = 0
x + 2 = 0 ==> x1 = - 2
2x^2 - 1 = 0 ==> x^2 = 1/2 ==> x2 = √2/2 ; x3 = - √2/2
Ответ:
3