3 years ago

Which equation is equivalent to the formula below

Mathematics

1 answer:

dusya [7]3 years ago

6 0

Answer:

Step-by-step explanation:

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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:

$a^2 +95a -500=0\\\therefore\: a^2 +100a -5a-500=0\\\therefore\: a(a +100) -5(a+100)=0\\\therefore\: (a +100)(a -5)=0\\\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\\therefore\: a = - 100\:\: or \:\: a = 5\\\\CASE\: (1)\:\\When\: a = - 100 \implies x^2 = - 100\\\therefore x=\pm \sqrt{-100}\\$