Question

Select all solutions of 𝑥^4 +6⁢𝑥^2 +5 =0.

Answer 1

Treat it as a quadratic in x^2: let y = x^2. Then y^2 + 6y + 5 = 0 = (y+1)(y+5), so y = -1 or y = -5. Thus
x^2 = -1 ⇒ x = ±i,
x^2 = -5 ⇒ x = ±i√5.

Solutions: x = ±i, ±i√5.