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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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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(B) | Q: 15 | Page no. 94
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Solution Find the Third Proportional to X/Y + Y/X and Sqrt(X^2 + Y^2) Concept: Proportions.
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