Question

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

Answer 1

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

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

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

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

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