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If the arithmetic, geometric and harmonic means between two positive real numbers be $A, G$ and $H$, then
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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 $G^2=A H$
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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