Question

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

Answer 1

The given quadratic equation $a^2{b}^2{x}^2-(a^2+b^2)x+1=0$ can be factorised as follows:

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

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