Question

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What are the solutions of the equation x4 + 95x2 - 500 = 0? Use factoring to solve.
x = tv5 and x = +10
x=tin 5 and x = 101
x= INV5 and x = +101
x==N5 and x = +10

Answer 1

Step-by-step explanation:

Given bi-quadratic equation is:

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

Substituting $x^2=a,$ given bi-quadratic equation reduces in the form of following quadratic equation:

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

Let us factorize the above quadratic equation:

$a^2 +95a -500=0\\

\therefore\: a^2 +100a -5a-500=0\\

\therefore\: a(a +100) -5(a+100)=0\\

\therefore\: (a +100)(a -5)=0\\

\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\

\therefore\: a = - 100\:\: or \:\: a = 5\\\\

CASE\: (1)\:\\

When\: a = - 100 \implies x^2 = - 100\\

\therefore x=\pm \sqrt{-100}\\

$

Since square root of a negative number cannot be found, so:

$x \neq \pm \sqrt{-100}\\

$

$CASE\: (2)\:\\

When\: a =5 \implies x^2 =5\\

\therefore x=\pm \sqrt{5}\\

$