Решите уравнение х^3+7х/х+8=8/х

1)ОДЗ: x≠-8

2)x³+7x = 8

x³+7x-8 = 0

x³-x+8x-8 = 0

x(x²-1)+8(x-1) = 0

x(x-1)(x+1)+8(x-1) = 0

(x-1)(x(x+1)+8) = 0

(x-1)(x²+x+8) = 0

1°)x1 = 1

2°)x²+x+8 = 0

D = b²-4ac = 1-4•8 < 0

∅

ответ: x = 1