Question

Solve the following quadratic equation:

a²b²x² + b²x – a²x – 1 = 0 

Answer 1

Given:

a²b²x² + b²x – a²x – 1 = 0 

⇒ b²x(a²x + 1) – 1(a²x + 1) = 0 

⇒ (b²x – 1)(a²x + 1) = 0 

⇒ (b²x – 1) = 0 or (a²x + 1) = 0 

⇒ `x = 1/b^2` or `x = (-1)/a^2` 

Hence, `1/b^2` and `(-1)/a^2` are the roots of the given equation.