Solve the following quadratic equation by factorization: a^2 b^2 … - Vidyadip

Question

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

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Answer

We have
$ a^2 b^2 x^2+b^2 x-a^2 x-1=0$
${\left[-1 \times a^2 b^2=-a^2 b^2 \Rightarrow-a^2 b^2=-a^2 \times b^2=-a^2 \times b^2\right]}$
$\Rightarrow a^2 b^2 x^2+b^2 x-a^2 x-1=0$
$\Rightarrow b^2 x\left(a^2 x+1\right)-1\left(a^2 x+1\right)=0$
$\Rightarrow\left(a^2 x+1\right)\left(b^2 x-1\right)=0$
$\Rightarrow a^2 x+1=0 \text { or } b^2 x-1=0$
$\Rightarrow\text{x}= -\frac{1}{\text{a}^2}$ and $\text{x}= \frac{1}{\text{b}^2}$ are the two root of the given equation.

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