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let (a+b)/c,(a+c)/b,(b+c)/a are in AP. Then prove that c(a+b),b(a+c),a(b+c) are also in AP.

let (a+b)/c,(a+c)/b,(b+c)/a are in AP. Then prove that c(a+b),b(a+c),a(b+c) are also in AP.

Grade:11

1 Answers

vikas
16 Points
5 years ago
given:   (a+b)/c,(a+c)/b,(b+c)/a are in AP
to prove: (a+b)/c,(a+c)/b,(b+c)/a are in AP
proof,
         since,common difference remain samein two successive term of an AP.
so
(a+c)/b – (a+b)/c = (b+c)/a – (a+b)/c
or (ac+c^2-ab-b^2)/bc =  (b^2+bc-a^2+ac)/ab
or (ac+c^2-ab-b^2)/c =  (b^2+bc-a^2+ac)/a
or b^2c+
 

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