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2 days ago

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

Mathematics

1 answer:

tester [12K]2 days ago

6 0

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

Explanation:

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

, we aim to find the solutions of the equation.

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

Thus, the equation transforms into

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

Factoring the equation results in:

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

$u=-1, u=-5$

Inserting back $x^{2} =u$ and allows us to solve for x.

Initially, we will substitute $u=-1$

Consequently, we find;

$x^{2} =-1$

$x=\sqrt{-1}$

$x=\pm i$

Similarly, by substituting $u=-5$ , we derive;

$x^{2} =-5$

$x=\sqrt{-5}$

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

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

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