Question

Solve the following quadratic equation by factorisation:

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

Answer 1

Given:

$$\begin{gathered} a^2{b}^2{x}^2+b^{2}x–a^{2}x–1=0 \\ \Rightarrow b^{2}x(a^{2}x+1)–1(a^{2}x+1)=0 \\ \Rightarrow (a^{2}x+1)(b^{2}x–1)=0 \\ \Rightarrow a^{2}x+1=0\text{and}{b}^{2}x–1=0 \\ \Rightarrow a^{2}x=-1\text{and}{b}^{2}x=1 \end{gathered}$$

Therefore, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{-}\mathbf{1}}{{\mathbf{a}}^{\mathbf{2}}}$ and $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{{\mathbf{b}}^{\mathbf{2}}}$ are the solution of given quadratic equation.