Question

find the solutions of x^4-x^2-2=0.

Answer 1

Let y = x^2. Then the equation becomes y^2 - y - 2 = 0, which factors as (y - 2)(y + 1) = 0. Thus y = 2 or y = −1.

So x^2 = 2 → x = ±√2, and x^2 = −1 → x = ±i.

Equivalently, x^4 - x^2 - 2 = (x^2 - 2)(x^2 + 1).