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

Solution:

Given: Equation is x⁴ - 9x² + 8 = 0

Let x² = u then the given equation becomes u² - 9u + 8 = 0

This is in the form ax² + bx + c= 0

We can solve by using quadratic formula for finding roots

x = {-b ± √(b² - 4ac)} / 2a

Here, a = 1, b = -9, c = 8

⇒ m = {-(-9) ± √((-9)² - 4(1)(8))} / 2(1)

⇒ m = {9 ± √(81 - 32)} / 2

⇒ m = {9 ± √49} / 2

⇒ m = {9 ± 7}/2

⇒ m = 16/2, 2/2

⇒ m = 8, 1 

⇒ x² = 8,1

⇒ x = ±2√2, ±1

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

Summary:

The solutions of the equation x⁴ - 9x² + 8 = 0 by using the substitution method are ±2√2, ±1.