Question

Solve the following equation by factorisation method:

a²b²x² − (a² + b²) x + 1 = 0

Answer 1

Given:

a²b²x² − (a² + b²) x + 1 = 0

(abx − 1) (abx − 1) or (abx − a) (bx − 1)

a²b²x² − (a² + b²) x + 1

(abx − 1)² = a²b²x² − 2abx + 1

(a²b²x² − a²x − b²x + 1)

(a²b²x² − a²x) − (b²x − 1)

a²x(b²x − 1) − 1(b²x − 1)

(b²x − 1) (a²x − 1) = 0

b²x − 1 = 0

⇒ x = `1/b^2`

a²x − 1 = 0

⇒ x = `1/a^2`

`x = 1/a^2 or x = 1/b^2`