Question

Решить уравнение x^6 - 9x^2 + 8 = 0

Answer 1

Пусть $t = x^2$.

$t^3 - 9t + 8 = 0\\t(t^2 - 1) - 8(t - 1) = 0\\(t - 1)(t(t + 1) - 8) = 0\\(t - 1)(t^2 + t - 8) = 0\\t = 1 \Rightarrow x = \pm 1\\t^2 + t - 8 = 0\\t = \frac{-1 \pm \sqrt{33}}{2}\\t \geq 0 \Rightarrow t = \frac{\sqrt{33} - 1}{2} \Rightarrow x = \pm \sqrt{\frac{\sqrt{33} - 1}{2}}$