#### 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

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