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# If P, Q, R Ands Are in Continued Proportion, Then Prove that (P3+Q3+R3) ( Q3+R3+S3) : : P : S - ICSE Class 10 - Mathematics

ConceptComponendo and Dividendo Properties

#### Question

If p, q, r ands are In continued proportion, then prove that (p3+q3+r3) ( q3+r3+s3) : : P : s

#### Solution

"p"/"q" = "q"/"r" = "r"/"s" = "k"

r = ks

q = kr = k2s

p = kq = k3s

LHS

("p"^3 + "q"^3 + "r"^3)/("q"^3 + "r"^3 + "s"^3)

= ("k"^9"s"^3 + "k"^6 "s"^3 + "k"^3"s"^3)/("k"^6"s"^3 + "k"^3"s"^3 + "s"^3)

= ("s"^3"k"^3("k"^6 + "k"^3 + 1))/("s"^3("k"^6 + "k"^3"s"^3 + "s"^3))

= "k"^3

RHS

"p"/"s" = ("k"^3"s")/"s" = "k"^3

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: 7

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Solution If P, Q, R Ands Are in Continued Proportion, Then Prove that (P3+Q3+R3) ( Q3+R3+S3) : : P : S Concept: Componendo and Dividendo Properties.
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