Question

Solve the following quadratic equations by factorization:

a²b²x² + b²x - a²x - 1 = 0

Answer 1

We have been given

a²b²x² + b²x - a²x - 1 = 0

b²x(a²x + 1) - 1(a²x + 1) = 0

(b²x - 1)(a²x + 1) = 0

Therefore,

b²x - 1 = 0

b²x = 1

`x=1/b^2`

or,

a²x + 1 = 0

a²x = -1

`x=-1/a^2`

Hence, `x=1/b^2` or `x=-1/a^2`