Solve the Following Quadratic Equation by Factorization
Question:
\[ a^2b^2x^2+b^2x-a^2x-1=0 \]Solution
Given,
\[ a^2b^2x^2+b^2x-a^2x-1=0 \]Grouping the terms:
\[ (a^2b^2x^2+b^2x)-(a^2x+1)=0 \]Taking common factors:
\[ b^2x(a^2x+1)-1(a^2x+1)=0 \] \[ (a^2x+1)(b^2x-1)=0 \]Therefore,
\[ a^2x+1=0 \] or \[ b^2x-1=0 \] \[ x=-\frac{1}{a^2} \] or \[ x=\frac{1}{b^2} \]