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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

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Question

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

Solution

`"u"/"v" = "v"/"w" = "w"/"x" = "a"`

w = ax

v = aw = a2

u = av = a3

LHS

`(2"u" + 3"x")/(3"u" + 4"x")`

`= (2"a"^3"x" + 3"x")/(3"a"^3"x" + 4"x")`

`= (2"a"^3 + 3)/(3"a"^3 + 4)`

RHS 

`(2"u"^3 + 3"v"^3)/(3"u"^3 + 4"v"^3)`

`= (2"a"^9"x"^3 + 3"a"^6"x"^3)/(3"a"^9"x"^3 + 4"a"^6"x"^3)`

`= (2"a"^3 + 3)/(3"a"^3 + 4)`

LHS = RHS. Hence , proved.

  Is there an error in this question or solution?

APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 8

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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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