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# If A, B, C and D Are in Proportion Prove that Sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((Xa^3 - 4yb^3)/(Xc^3 - 5yd^3))^(1/3) - ICSE Class 10 - Mathematics

#### Question

If a, b, c and d are in proportion prove that sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((xa^3 - 4yb^3)/(xc^3 - 5yd^3))^(1/3)

#### Solution

a, b, c and d are in proportion

a/b = c/d = k (say)

Then a = bk and c = dk

L.H.S = sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = sqrt((4(bk)^2 + 9b^2)/(4(dk)^2 + 9d^2)) = sqrt((b^2(4k^2 + 9))/(d^2(4k^2 + 9))) = b/d

R.H,S = ((xa^3 - 5yb^3)/(xc^3 - 5yd^3))^(1/3) = [(x(bk)^3 - 5yb^3)/(x(dk)^3 - 5yd^3)]^(1/3)

= [(b^3(xk^3 - 5y))/(d^3(xk^3 - 5y))]^(1/3)

= [b^3/d^3]^(1/3) = b/d`

Hence LHS = RHS

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#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7B | Q: 19.2

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Solution If A, B, C and D Are in Proportion Prove that Sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((Xa^3 - 4yb^3)/(Xc^3 - 5yd^3))^(1/3) Concept: Proportions.
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