If M: N is the Duplicate Ratio of M + X: N + X; Show that X2 = Mn. - Mathematics

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

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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 7 Ratio and Proportion (Including Properties and Uses)
Exercise 7 (A) | Q 27 | Page 88