Question

What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.

Answer 1

Answer:

x = i and x = i$\sqrt{5}$

Step-by-step explanation:

Given

$x^{4}$ + 6x² + 5 = 0

Using the substitution u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Convert solutions back into terms of x

x² = - 1 ⇒ x = $\sqrt{-1}$ = i

x² = - 5 ⇒ x = $\sqrt{-5}$ = i$\sqrt{5}$