Solve this

Question:

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

 

Solution:

Given :

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

$\Rightarrow b^{2} x\left(a^{2} x+1\right)-1\left(a^{2} x+1\right)=0$

$\Rightarrow\left(b^{2} x-1\right)\left(a^{2} x+1\right)=0$

$\Rightarrow\left(b^{2} x-1\right)=0$ or $\left(a^{2} x+1\right)=0$

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

Hence, $\frac{1}{b^{2}}$ and $\frac{-1}{a^{2}}$ are the roots of the given equation.

 

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