Question

What are the solutions of the equation x4 – 9x2 + 8 = 0? Use u substitution to solve.

x = 1 and x = 2 StartRoot 2 EndRoot
x = ±1 and x = plus-or-minus 2 StartRoot 2 EndRoot
x = ±i and x = plus-or-minus 2 i StartRoot 2 EndRoot
x = ±i and x = 2 StartRoot 2 EndRoot

Answer 1

B

Explanation:

Answer 2

Option (2)

Explanation:

Given equation is,

x⁴- 9x² + 8 = 0

Let x² = t

By substituting the value of x²= t in the equation,

t² - 9t + 8 = 0

t² - 8t - t + 8 = 0

t(t - 8) - 1(t - 8) = 0

(t - 1)(t - 8) = 0

(t - 1) = 0 ⇒ t = 1

(t - 8) = 0 ⇒ t = 8

Since, t = x²

x² = 1 ⇒ x = ±1

x² = 8 ⇒ x = ±2√2

Therefore, Option (2) will be the correct option.