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

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Question

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

Sum
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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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Chapter 7: Ratio and proportion - Exercise 7A [Page 116]

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Nootan Mathematics [English] Class 10 ICSE
Chapter 7 Ratio and proportion
Exercise 7A | Q 20. | Page 116
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