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# What are the solutions of the equation x^{4} - 9x^{2} + 8 = 0? Use u substitution to solve.

**Solution:**

Given: Equation is x^{4} - 9x^{2} + 8 = 0

Let x^{2} = u then the given equation becomes u^{2} - 9u + 8 = 0

This is in the form ax^{2} + bx + c= 0

We can solve by using quadratic formula for finding roots

x = {-b ± √(b^{2} - 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

⇒ x^{2 }= 8,1

⇒ x = ±2√2, ±1

## What are the solutions of the equation x^{4} - 9x^{2} + 8 = 0? Use u substitution to solve.

**Summary:**

The solutions of the equation x^{4} - 9x^{2} + 8 = 0 by using the substitution method are ±2√2, ±1.

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