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Question: Answered & Verified by Expert
If the arithmetic, geometric and harmonic means between two positive real numbers be $A, G$ and $H$, then
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Options:
  • A $A^2=G H$
  • B $H^2=A G$
  • C $G=A H$
  • D $G^2=A H$
Solution:
1813 Upvotes Verified Answer
The correct answer is: $G^2=A H$
$A=\frac{a+b}{2}, G=\sqrt{a b}$ and $H=\frac{2 a b}{a+b}$
Then $G^2=a b\ldots(i)$
and $A H=\left(\frac{a+b}{2}\right) \cdot \frac{2 a b}{a+b}=a b \ldots(ii)$
From (i) and (ii), we have $G^2=A H$

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