Question

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

x = i and x = 5
x=t i and x = = 15
x=+ -1 and x = 1 -5
X= + -1 and x = 1 - 5

Answer 1

x = i and x = i
`√(5)`

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 =
`√(-1)` = i

x² = - 5 ⇒ x =
`√(-5)` = i
`√(5)`