Solve the following quadratic equation by factorization:
$a^2b^2x^2+b^2x-a^2x-1=0$

Given:

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

To do:

We have to solve the given quadratic equation.

Solution:

$a^2b^2x^2+b^2x-a^2x-1=0$

To factorise $a^2b^2x^2+b^2x-a^2x-1=0$, we have to find two numbers $m$ and $n$ such that $m+n=b^2-a^2$ and $mn=a^2b^2(-1)=-a^2b^2$.

If $m=b^2$ and $n=-a^2$, $m+n=b^2-a^2$ and $mn=b^2\times(-a^2)=-a^2b^2$.

$a^2b^2x^2+b^2x-a^2x-1=0$

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

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

$a^2x+1=0$ or $b^2x-1=0$

$a^2x=-1$ or $b^2x=1$

$x=-\frac{1}{a^2}$ or $x=\frac{1}{b^2}$

The values of $x$ are  $-\frac{1}{a^2}$ and $\frac{1}{b^2}$.

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Updated on: 10-Oct-2022

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