Question

What are the solutions of the equation x4 95x2 â€"" 500 = 0? Use factoring to solve.

Answer 1

All the values of the x for the given function are $\sqrt{5},-\sqrt{5}, 10i$ and $-10i$.

Given-

Given function is,

$x^{4}+95x^2-500=0$

Rewrite the equation,

$(x^2)^2+95x^2-500=0$

Let u in place of $x^2$ and rewrite the equation in the form of u,

$u^2+95u-500=0$

Break the 95 in factors and rewrite the equation,

$u^2+100u-5u-500=0$

$u(u+100)-5(u+100)=0$

$(u+100)(u-5)=0$

Replace the value of u with $x^2$,

$(x^2+100)(x^2-5)=0$

It is known that If any individual factor on the left side of the equation is equal to zero then the entire expression will be equal to zero. therefore we get,

$x^2-5=0$

further, solve it,

$x^2=5$

$x=\sqrt{5},-\sqrt{5}$

And another factor is

$x^2+100=0$

$x^2=-100$

$x=10i,-10i$

Hence, all the values of the x for the given function are $\sqrt{5},-\sqrt{5},$  $10i ,$ and  $-10i$.

For more about the factorization, follow the link below-

brainly.com/question/6810544