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Question

If the harmonic mean between a and b be H, then the value of 1H−a+1H−b is

A
a+b
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B
ab
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C
1a+1b
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D
1a1b
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Solution

The correct option is C 1a+1b
Putting H=2aba+b, we have 1Ha+1Hb
=1(2aba+ba)+1(2aba+bb)=a+baba2+a+babb2

=(a+bba)(1a1b)=(a+bba)(baab)=a+bab=1a+1b.

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