Question

If m : n is the duplicate ratio of m + x : n + x; show that x² = mn.

Answer 1

`m/n = (m + x)^2/(n + x)^2`

`m/n = (m^2 + x^2 + 2mx)/(n^2 + x^2 + 2nx)`

mn² + mx² + 2mnx = m²n + nx² + 2mnx

mn² – m²n + mx² – nx² = 0

mn(m – n) – x²(m – n) = 0

x²(m – n) = mn(m – n)

x² = mn