#### Question

If m: n is the duplicate ratio of m + x: n + x; show that x^{2} = mn.

#### Solution

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

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

`mn^2 + mx^2 + 2mnx = m^2n + nx^2 + 2mnx`

`x^2(m - n) = mn(m - n)`

`x^2 (m - n) = mn(m - n)`

`x^2 = mn`

Is there an error in this question or solution?

Solution If M: N is the Duplicate Ratio of M + X: N + X; Show that X2 = Mn. Concept: Ratios.