Question

What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.

Answer 1

`x = \: x = \pm \: √(2) i \: or \: x = \pm \: i`

Step-by-step explanation

`{x}^(4) + 3 {x}^(2) + 2 = 0`

`{ ({x}^(2)) }^(2) + 3( {x}^(2)) + 2 = 0`

Let

`u = {x}^(2)`

Then the equation becomes:

`{u}^(2) + 3u + 2 = 0`

`{u}^(2) + 3u + 2 = 0`

`{u}^(2) + 2u +u + 2 = 0`

Factor:

`{u}(u + 2)+ 1(u + 2) = 0`

`(u + 1)(u + 2) = 0`

`u = - 1`

or

`u = - 2`

This implies that

`{x}^(2) = - 1 \implies \: x = \pm \: i`

or

`{x}^(2) = - 2 \implies \: x = \pm \: √(2) i`