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