Question

find the solutions of x^4-x^2-2=0 and say them all

Answer 1

Treat it as a biquadratic. Let y = x^2, then

y^2 - y - 2 = 0 = (y - 2)(y + 1),

so y = 2 or y = -1. Thus

x^2 = 2 ⇒ x = ±√2,
x^2 = -1 ⇒ x = ±i.

All solutions: √2, −√2, i, −i.