Solve the following quadratic equation by factorization:

$a(x^2+1)-x(a^2+1)=0$

Given:

Given quadratic equation is $a(x^2+1)-x(a^2+1)=0$.

To do:

We have to solve the given quadratic equation.

Solution:

$a(x^2+1)-x(a^2+1)=0$

$ax^2+a-a^2x-x=0$

$ax(x-a)-1(x-a)=0$

$(ax-1)(x-a)=0$

$ax-1=0$ or $x-a=0$

$ax=1$ or $x=a$

$x=\frac{1}{a}$ or $x=a$

The values of $x$ are $\frac{1}{a}$ and $a$. 

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Updated on: 10-Oct-2022

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