Question

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

Answer 1

u=x^2 and the solutions are x= + or - the squareroot of 2 and x= + or - 1

Answer 2

Answer: x = ± i , x = ±√2i are solution .

Explanation:

Given :
`x^(4) +3x^(2) +2=0`, use u substitution to solve.

To find : what are the solutions of the equation .

Solution : We have given that
`x^(4) +3x^(2) +2=0`.

Let consider
`x^(2)` = u .

Substitute u =
`x^(2)` in given equation .

`u^(2) + 3u +2=0`.

On factoring

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

Taking common

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

On grouping

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

Now, u+1 = 0 ⇒ u = -1.

u+2 = 0 ⇒ u = -2.

In term of x, plugging
`x^(2)` = u.

`x^(2)` = -1 ;
`x^(2)` = -2.

taking square root both side

x = ± i

x = ±√2i.

Therefore, x = ± i , x = ±√2i are solution .