Question

What are the soultions of the equation x^4 - 9x^2 + 8 = 0? Use u substitution to solve.​

Answer 1

Explanation:

Let u=x^2.

Notice that

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

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

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

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

`u = 8`

`u = 1`

Replace x^2= u

`{x}^(2) = 8`

`x = ±2 √(2)`

`{x}^(2) = 1`

`x = ±1`

So our answer is

`±1 \:`

and

`±2 √(2)`