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If U, V, W, and X Are in Continued Proportion, Then Prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3) - ICSE Class 10 - Mathematics

Question

If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3)

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

Solution

p : q : : q : r ⇒ q2 = pr

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

LHS

("pqr")^2 (1/"p"^4 + 1/"q"^4 + 1/"r"^4)

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

= "q"^6 (("q"^4"r"^4 + "q"^8 + "p"^4"q"^4)/("q"^8"q"^4))

= "q"^6 (("r"^4 + "q"^4 + "p"^4)/"q"^8)

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

LHS = RHS , Hence Proved.

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

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Solution If U, V, W, and X Are in Continued Proportion, Then Prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3) Concept: Proportions.
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