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Find the Third Proportional to `X/Y + Y/X` and `Sqrt(X^2 + Y^2)` - ICSE Class 10 - 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 Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7B | Q: 15

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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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