Question

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

Answer 1

`x = \pm 2√(2) \: or \: {x}= \pm1`

Step-by-step explanation

Given;

`{x}^(4) - 9 {x}^(2) +8 = 0`

We can rewrite as

`({x}^(2) )^(2) - 9 {x}^(2) +8 = 0`

Let

`u = {x}^(2)`

This implies that,

`u^(2) - 9u +8 = 0`

This implies that,

`u^(2)-u - 8u +8 = 0`

`u(u - 1) - 8(u - 1) = 0`

`(u - 1)(u - 8) = 0`

`u = 8 \: or \: u = 1`

But

`u = {x}^(2)`

This implies that,

`{x}^(2) = 8 \: or \: {x}^(2) = 1`

`x = \pm √(8) \: or \: {x}= \pm √(1)`

`x = \pm 2√(2) \: or \: {x}= \pm1`