Question

Solve the following quadratic equations by factorization method:
$a^2{b}^2{x}^2-(a^2+b^2)x+1=0$

• A. $\{\frac{1}{b^2},\frac{1}{a^2}\}$
• B. $\{\frac{-1}{b^2},\frac{1}{a^2}\}$
• C. $\{\frac{1}{b^2},\frac{-1}{a^2}\}$
• D. None of these

Answer 1

The correct option is C $\{\frac{1}{b^2},\frac{-1}{a^2}\}$

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

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

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

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

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

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

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