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Find the Third Proportional to a - B and A^2 - B^2 - Mathematics

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Question

Find the third proportional to a - b and `a^2 - b^2`

Solution

Let the third proportional to a - b and `a^2 - b^2` be x

⇒  a - b, a2 - b2, x are in continued proportion.

⇒ a - b : a2 - b2 = a2 - b2 : x

`=> (a - b)/(a^2 - b^2) = (a^2 - b^2)/x`

`=> x = (a^2 - b^2)^2/(a - b)`

`=> x = ((a + b)(a - b)(a^2 - b^2))/(a - b)`

`=> x = (a + b)(a^2 - b^2)`

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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: 2.2 | Page no. 94
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Find the Third Proportional to a - B and A^2 - B^2 Concept: Ratios.
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