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If 1/a, 1/b, 1/c are in A.P. then prove that b+c/a, c+a/b, a+b/c are also in a.p.

If 1/a, 1/b, 1/c are in A.P. then prove that b+c/a, c+a/b, a+b/c are also in a.p.

Grade:12th pass

1 Answers

Arun
25758 Points
4 years ago

given: 1/a , 1/b and 1/c are in AP

multiplying each term by (a+b+c) will also result as an AP.

(a+b+c) / a , (a+b+c)/b and (a+b+c)/c must form an AP

subtracting 1 from each term is also an AP

therefore

(a+b+c) / a -1 , (a+b+c)/b -1 and (a+b+c)/c -1  is also an AP.

therefore (b+c)/a , (a+c)/b and (a+b)/c is an AP.

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