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If a, b, c are in continued proportion, then prove that b/b+c=a-b/a-c |
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Answer» Answer: b/b+c=a-b/a-c Step-by-step explanation: a, b, c are in continued proportion => a/b = b/c = K => a = bK & b = cK => a = CK² To be Proved that b/(b + c) = (a - b)/(a - c) LHS = b/(b + c) = cK/(cK + c) = K/(K + 1) RHS (a - b)/(a - c) = (cK² - cK) /(cK² - c) = K(K - 1) /( K² - 1) = K (K - 1) / ( (K + 1)(K - 1) ) = K /(K + 1) LHS = RHS b/b+c=a-b/a-c |
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