Question

Solve the following equation by factorisation method:

abx² − (a² + b²)x + ab = 0

Answer 1

Given:

abx² − (a² + b²)x + ab = 0

abx² − a²x − b²x + ab = 0

(abx² − a²x) − (b²x − ab) = 0

ax(bx − a) − b(bx − a) = 0

(bx − a) (ax − b) = 0

bx − a = 0

⇒ x = `a/b`

ax − b = 0

⇒ x = `b/a`

`x = a/b or x = b/a`