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Question
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
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Solution
Let the required third proportional be p.
`=> x/y + y/x, sqrt(x^2 + y^2)`, p are in continued proportion
`=> x/y + y/x : sqrt(x^2 + y^2) = sqrt(x^2 + y^2) : p`
`=> p(x/y + y/x) = (sqrt(x^2 + y^2))^2`
`=> p((x^2 + y^2)/(xy)) = x^2 + y^2`
`=>` p = xy
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