a, g, h are the arithmetic mean,geometric mea | vedclass

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(C) Given that $a, g, h$ are the arithmetic mean,geometric mean,and harmonic mean of two positive numbers $x$ and $y$ respectively.We have $a = \frac{

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$g$ is the geometric mean between $a$ and $h$

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(C) Given that $a, g, h$ are the arithmetic mean,geometric mean,and harmonic mean of two positive numbers $x$ and $y$ respectively.We have $a = \frac{x + y}{2}$,$g = \sqrt{xy}$,and $h = \frac{2xy}{x + y}$.Now,calculate $g^2$:$g^2 = (\sqrt{xy})^2 = xy$ ...$(i)$Next,calculate the product $ah$:$ah = \left(\frac{x + y}{2}\right) \cdot \left(\frac{2xy}{x + y}\right) = xy$ ...(ii)Comparing equations $(i)$ and (ii),we get $g^2 = ah$,which implies $g = \sqrt{ah}$.This confirms that $g$ is the geometric mean between $a$ and $h$.

$a, g, h$ are the arithmetic mean,geometric mean,and harmonic mean between two positive numbers $x$ and $y$ respectively. Identify the correct statement among the following:

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