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If X and Y Be Unequal and X: Y is the Duplicate Ratio of X + Z and Y + Z, Prove that Z is Mean Proportional Between X and Y. - ICSE Class 10 - Mathematics

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Question

If x and y be unequal and x: y is the duplicate ratio of x + z and y + z, prove that z is mean proportional between x and y.

Solution

Given `x/y = (x + z)^2/(y + z)^2`

`x(y^2 + z^2 + 2yz) = y(x^2 + z^2 + 2xy)`

`y^2 + xz^2 + 2xyz = x^y + yz^2 + 2xyz` 

`xy^2 + xz^2 = yz^2 - xz^2`

`xy(y - x) = z^2(y - x)`

`xy = z^2`

Hence z is mean proportional between x and y

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APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7D | Q: 11

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Solution If X and Y Be Unequal and X: Y is the Duplicate Ratio of X + Z and Y + Z, Prove that Z is Mean Proportional Between X and Y. Concept: Proportions.
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