Question

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

Answer 1

The answer is the second option

Explanation:

Let u=x^2.

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

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

`(u - 1)(u - 8)`

`u = 1`

`u = 8`

Set this equal to x^2

`{x}^(2) = 1`

`x = 1`

or

`x = - 1`

`{x}^(2) = 8`

`x = 2 √(2)`

or

`x = - 2 √(2)`