Question

Solve the quadratic equation : $a^2{b}^2{x}^2+b^{2}x-a^{2}x-1=0$.
[CBSE.2005,2008]

Answer 1

Given,

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

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

$a=a^2{b}^2,b=(b^2-a^2),c=-1$

$x=\frac{-(b^2-a^2)\pm \sqrt{{(b^2-a^2)}^2-4a^2{b}^2(-1)}}{2a^2{b}^2}$

$=\frac{-(b^2-a^2)\pm \sqrt{{(b^2-a^2)}^2+4a^2{b}^2}}{2a^2{b}^2}$

$=\frac{-(b^2-a^2)\pm (a^2+b^2)}{2a^2{b}^2}$

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