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# Find the Third Proportional to X/Y + Y/X and Sqrt(X^2 + Y^2) - Mathematics

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#### Question

Find the third proportional to x/y + y/x and sqrt(x^2 + y^2)

#### Solution

Let the required third proportional be p

=> x/y + y/x, sqrt(x^2 + y^2), p are in contined 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))0 = x^2 + y^2

=> p = xy

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