Question

Solve the following quadratic equations by factorization:

a²x² – 3abx + 2b² = 0

Answer 1

a²x² - 3abx + 2b² = 0

⇒ a²x² - 2abx - abx + 2b² = 0

⇒ ax(ax - 2b) - b(ax - 2b) = 0

⇒ (ax - b)(ax - 2b) = 0

Therefore,

ax - b = 0

ax = b

x = `b/a`

or,

ax - 2b = 0

ax = 2b

x = `(2b)/a`

Hence, x = `b/a` or x = `(2b)/a`.