Question
Solve the following quadratic equation: $a^2b^2x^2 + b^2x - a^2x - 1= 0$
✓
Answer
$a^2b^2x^2 + b^2x - a^2x - 1= 0$
$\Rightarrow b^2x(a^2x + 1) - 1(a^2x + 1) = 0$
$\Rightarrow (a^2x + 1)(b^2x - 1) = 0$
$\Rightarrow (a^2x + 1) = 0$ or $(b^2x - 1) = 0$
$\Rightarrow\text{x}=\frac{-\text{1}}{\text{a}^2}$ or $\text{x}=\frac{\text{1}}{\text{b}^2}$
Hence, $\frac{-\text{1}}{\text{a}^2}$ and $\frac{\text{1}}{\text{b}^2}$ are the roots of the given equation.
$\Rightarrow b^2x(a^2x + 1) - 1(a^2x + 1) = 0$
$\Rightarrow (a^2x + 1)(b^2x - 1) = 0$
$\Rightarrow (a^2x + 1) = 0$ or $(b^2x - 1) = 0$
$\Rightarrow\text{x}=\frac{-\text{1}}{\text{a}^2}$ or $\text{x}=\frac{\text{1}}{\text{b}^2}$
Hence, $\frac{-\text{1}}{\text{a}^2}$ and $\frac{\text{1}}{\text{b}^2}$ are the roots of the given equation.
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