(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)