If the arithmetic,geometric and harmonic mean | vedclass

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(D) Let the two positive real numbers be $a$ and $b$.The arithmetic mean is $A = \frac{a + b}{2}$.The geometric mean is $G = \sqrt{ab}$.The harmonic m

Vedclass · Accepted Answer

$G^2 = AH$

Vedclass · Answer

(D) Let the two positive real numbers be $a$ and $b$.The arithmetic mean is $A = \frac{a + b}{2}$.The geometric mean is $G = \sqrt{ab}$.The harmonic mean is $H = \frac{2ab}{a + b}$.Now,calculate $G^2$:$G^2 = (\sqrt{ab})^2 = ab$.Next,calculate $AH$:$AH = \left( \frac{a + b}{2} ight) 	imes \left( \frac{2ab}{a + b} ight) = ab$.Since both $G^2$ and $AH$ are equal to $ab$,we conclude that $G^2 = AH$.

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

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