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If X, Y, Z Are in Continued Proportion, Prove that `(X + Y)^2/(Y + Z)^2 = X/Z` - ICSE Class 10 - Mathematics

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Question

If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`

Solution

∵ x,y,z are in continued proportion,

`∴ x/y = y/z => y^2 = zx .....(1)`

`(x + y)/y = (y + z)/z`       (By componendo)

`=> (x + y)^2/(y + z) = y/z`     (By alternendo)

`=> (x + y)^2/(y + z)^2  = y^2/z^2 => (x + y)^2/(y + z)^2 = (zx)/z^2`

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

Hence Proved

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APPEARS IN

 2009-2010 (March) (with solutions)
Question 8.2 | 3.00 marks

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Solution If X, Y, Z Are in Continued Proportion, Prove that `(X + Y)^2/(Y + Z)^2 = X/Z` Concept: Proportions.
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