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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"^2 - "q"^2 + "r"^2 = "q"^4 (1/"p"^2 - 1/"q"^2 - 1/"r"^2)`

Solution

p : q :: q : r ⇒ q2 = pr

`"p"^2 - "q"^2 + "r"^2 = "q"^4 (1/"p"^2 - 1/"q"^2 - 1/"r"^2)`

RHS

`"q"^4 (1/"p"^2 - 1/"q"^2 - 1/"r"^2)`

`= "q"^4 (("q"^2"r"^2 - "p"^2 "r"^2 + "p"^2"q"^2)/("p"^2"q"^2"r"^2))`

`= "q"^4 "q"^2 (("r"^2 - "q"^2 + "p"^2)/("q"^2"q"^4))`

= p2 - q2 + r2 = LHS

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: 9.4

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