Question

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

Answer 1

$$\begin{gathered} \begin{array}{l}\mathrm{Given}:\\ a^2{b}^2{x}^2+b^{2}x-a^{2}x-1=0 \\ \Rightarrow b^{2}x(a^{2}x+1)-1(a^{2}x+1)=0 \\ \Rightarrow (b^{2}x-1)(a^{2}x+1)=0 \\ \Rightarrow (b^{2}x-1)=0\text{or (}{a}^{2}x+1)=0 \\ \Rightarrow x=\frac{1}{b^2}\text{or}x=\frac{-1}{a^2} \\ \mathrm{H}\text{ence,}\frac{1}{b^2}\text{and}\frac{-1}{a^2}\text{are the roots of the given equation.}\end{array} \end{gathered}$$