Question

Solve the given quadratic equation by factorization method
$a^2{b}^2{x}^2+b^{2}x-a^{2}x-1=0$

Answer 1

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

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

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

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