Решите уравнение (x^2-x-1) ^2-x^3=5

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(x^2 - x - 1) ^2 - x^3 = 5

(x^2 - x - 1) (x^2 - x - 1) - x^3 - 5 = 0

x^4 - x^3 - x^2 - x^3 + x^2 + x - x^2 + x + 1 - x^3 - 5 = 0

x^4 - 3x^3 - x^2 + 2x - 4 = 0

(x^2 - 2x - 4) * (x^2 - x + 1) = 0

[x^2 - 2x - 4 = 0

[x^2 - x + 1 = 0

1) x^2 - 2x - 4 = 0

D = 4 - 4*1 * (-4) = 20

x1 = (2 + sqrt (20)) / 2 = (2 + 2*sqrt (5)) / 2 = 2 (1 + sqrt (5)) / 2 = 1 + sqrt (5)

x2 = 1 - sqrt (5)

2) x^2 - x + 1 = 0

D = 1 - 4*1*1 = - 3 < 0 - корней нет.

Ответ: 1 + sqrt (5) ; 1 - sqrt (5)