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# If A, B, C, D Are in Proportion , Then Prove that √ a 2 + 5 C 2 B 2 + 5 D 2 = a B - Algebra

Sum

If a, b, c, d   are in proportion , then prove that
sqrt[( a^2 + 5c^2)/( b^2 + 5d^2)] = a/d

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#### Solution

It is given that a, b, c, d are in proportion.

therefore a/b = c/d = k

⇒ a = bk , c = dk

sqrt[( a^2 + 5c^2)/( b^2 + 5d^2)] = sqrt[(bk)^2 + 5(dk)^2]/(b^2 + 5d^2 ) = sqrt[k^2( b^2 + 5d^2)]/(b^2 + 5d^2) = sqrt(k^2) = k                                                ....(1)

a/b = [bk]/b = k                                                        .....(2)
From (1) and (2), we get
sqrt[ a^2 + 5c^2]/[b^2 + 5d^2] = a/b

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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 4 Ratio and Proportion
Problem Set 4 | Q 9.2 | Page 78
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