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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: 

(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)

Solution

p : q :: q : r => q2 = pr1

LHS (p2 _ q2)( q2 + r2
= (p2 -(pr)2)(pr)2 + r2
= p3r - p2r2 + p2r2 - pr3 
= pr (p2 - r2)

RHS

(q2 - r2)(p2 + q2

= ((pr)2-r2 )(p2+ (pr)2)

= p3r - p2r2 + p2t2 - pr3

= pr(p2 - r2

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: 9.1

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