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Question

If the arithmetic mean of two positive numbers is A, their geometric mean is G and harmonic mean is H, then His equal to


A

G2A

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B

GA2

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C

A2G2

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D

AG2

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Solution

The correct option is A

G2A


Find the value of the harmonic mean H:

Given that the arithmetic mean of two positive numbers is A, their geometric mean is G .

Let a and b be two numbers.

The arithmetic mean (AM) A=(a+b)2

The geometric mean (GM)G=ab

The harmonic mean (HM) H=2ab(a+b)

=G2A

Hence, the correct option is A.


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