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If H(1) and H(2) are two harmonic means ...

If `H_(1)` and `H_(2)` are two harmonic means between two positive numbers a and b `(a != b)` , A and G are the arithmetic and geometric menas between a and b , then `(H_(2)+H_(1))/(H_(2)H_(1))` is

A

`(2A)/(G)`

B

`A/(2G^(2))`

C

`A/G^(2)`

D

`(2A)/(G^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Let a, b be two positive numbers and `1/a, 1/H_(1),1/H_(2),1/b`" are in A.P."`
`1/H_(1)+1/H_(2)=(a+b)/(ab)=(2A)/(G^(2))`
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