Question

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

Answer 1

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

Step-by-step 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 .