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# If A, B, C Are in Continued Proportion , Then Prove that B B + C = a − B a − C - Algebra

Sum

If   a, b, c  are in continued proportion , then prove that

b/[b+c] = [a-b]/[a-c]

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#### Solution

a, b, c are in continued proportion.
therefore a/b = b/c = k

⇒ a = bk, b = ck

⇒ a = bk = ck xx k = ck^2

b/[ b + c] =  [ck]/[ ck + c ] = [ck]/[ c( k + 1)] = k/( k + 1)                  ...........(1)

[ a - b]/[ a - c ] = [ ck^2 - ck]/[ ck^2 - c ] = [ck( k -1)]/[c(k^2 - 1)] = [k( k -1)]/[(k-1)(k+1)] = k/(k + 1)                                                                                            .............(2)

From (1) and (2), we get

b/[b+c] = [a-b]/[a-c]

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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 4 Ratio and Proportion
Problem Set 4 | Q 10.2 | Page 79
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