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If a, b, c are in H.P., show that a/b+c, b/c+a, c/a+b are also in H.P?

 If a, b, c are in H.P., show that a/b+c, b/c+a, c/a+b are also in H.P?

Grade:11

1 Answers

Latika Leekha
askIITians Faculty 165 Points
8 years ago
Hello student,
Given that a, b and c are in H.P.
So, 1/a, 1/b and 1/c are in A.P.
Hence, (a+b+c)/a, (a+b+c)/b, (a+b+c)/c are in A.P.
So, 1+(b+c)/a, 1+(c+a)/b, 1+(a+b)/c are in A.P.
This means (b+c)/a, (c+a)/b, (a+b)/c are in A.P.
So, a/(b+c), b(/c+a), c/(a+b) are also in H.P.
Hence, proved!!

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