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If P, Q and R in Continued Proportion, Then Prove the Following: - ICSE Class 10 - Mathematics

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Question

If p, q and r in continued proportion, then prove the following: 

(p + q + r )(p - q + r) = p2 + q2 + r2 

Solution

p : q :: q : r  ⇒ q2 = pr  

(p + q + r )(p - q + r) = p2 + q2 + r2 

LHS

(p + q + r)(p - q + r)

= p2 + pq + pr - pq - q2 - qr + pr + qr + r2

= p2 + 2pr - q2 + r2

= p2 + 2q2 - q2 + r2

= p2 + q2 + r2 = RHS 

LHS = RHS. Hence, proved. 

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 9.2

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Solution If P, Q and R in Continued Proportion, Then Prove the Following: Concept: Proportions.
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