Решыть уравнение: (x^{2} +6x-7)(x^{2}+6x+8)=16

(x^{2} +6x-7)(x^{2}+6x+8)=16

замена x^2 + 6x - 7 = t

t*(t + 15) = 16

t^2 + 15 t - 16 = 0

D= 15^2 + 4*16 = 289 = 17^2

t12 = (-15 +- 17)/2 = 1   -16

1/ x^2+6x -7 = 1

x^2 + 6x - 8 = 0

D = 36 + 32 = 68

x12 = (-6 +- √68) / 2 = (-6 +- 2√17)/2 = -3 +- √17

2/ x^2 + 6x - 7 = - 16

x^2 + 6x + 9 = 0

(x + 3)^2 = 0

x = -3

ответ -3 + √17,  -3 - √17, -3