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