Question

What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.

Answer 1

The solutions of the equation are $x=\pm i, x=\pm \sqrt{5}i$

Explanation:

Given that the equation is $x^{4}+6 x^{2}+5=0$

We need to determine the solutions of the equation.

Let us substitute $x^{2} =u$ and $x^4=u^2$

Thus, the equation becomes,

$u^{2}+6 u+5=0$

Factoring the equation, we get;

$(u+1)(u+5)=0$

      $u=-1, u=-5$

Substituting back $x^{2} =u$ and solve for x.

First, we shall substitute $u=-1$

Thus, we get;

$x^{2} =-1$

$x=\sqrt{-1}$

$x=\pm i$

Similarly, substituting $u=-5$, we get;

$x^{2} =-5$

$x=\sqrt{-5}$

$x=\pm \sqrt{5}i$

Thus, the solutions of the equation are $x=\pm i, x=\pm \sqrt{5}i$