(x^2+x-1)*(x^2+x+2)=40.Помогите плиз.Пусть x^2+x-1=t?????

Question

(x^2+x-1)*(x^2+x+2)=40.Помогите плиз.
Пусть x^2+x-1=t?????

Answer 1

X² + x - 1 = t

x² + x + 2 = x² + x - 1 + 3 = t + 3

t(t+3) = 40

t² + 3t - 40 = 0
D = 9 + 160 = 169 

t1 = (-3-13)/2 = -8
t2 = (-3+13)/2 = 5

1) x² + x - 1 = -8
x² + x + 7 = 0
D = 1 - 28 = -27 < 0
нет решений в R

2) x² + x - 1 = 5
x² + x - 6 = 0
D = 1 + 24 = 25
x1 = (-1-5)/2 = -3
x2 = (-1+5)/2 = 2

Ответ: -3 и 2