Answer: x = ± i , x = ±√2i are solution .
Step-by-step explanation:
Given : [tex]x^{4} +3x^{2} +2=0[/tex], use u substitution to solve.
To find : what are the solutions of the equation .
Solution : We have given that [tex]x^{4} +3x^{2} +2=0[/tex].
Let consider [tex]x^{2}[/tex] = u .
Substitute u = [tex]x^{2}[/tex] in given equation .
[tex]u^{2} + 3u +2=0[/tex].
On factoring
[tex]u^{2} + 2u+1u +2=0[/tex].
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 [tex]x^{2}[/tex] = u.
[tex]x^{2}[/tex] = -1 ; [tex]x^{2}[/tex] = -2.
taking square root both side
x = ± i
x = ±√2i.
Therefore, x = ± i , x = ±√2i are solution .
Answer:
u=x^2 and the solutions are x= + or - the squareroot of 2 and x= + or - 1
