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(C) The arithmetic mean of $a$ and $b$ is $A = \frac{a + b}{2}$.The geometric mean of $a$ and $b$ is $G = \sqrt{ab}$.Then,$A - G = \frac{a + b}{2} - \

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$[\frac{\sqrt{a} - \sqrt{b}}{\sqrt{2}}]^2$

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(C) The arithmetic mean of $a$ and $b$ is $A = \frac{a + b}{2}$.The geometric mean of $a$ and $b$ is $G = \sqrt{ab}$.Then,$A - G = \frac{a + b}{2} - \sqrt{ab} = \frac{a + b - 2\sqrt{ab}}{2}$.Since $a = (\sqrt{a})^2$ and $b = (\sqrt{b})^2$,we have $A - G = \frac{(\sqrt{a})^2 + (\sqrt{b})^2 - 2\sqrt{a}\sqrt{b}}{2} = \frac{(\sqrt{a} - \sqrt{b})^2}{2}$.This can be rewritten as $[\frac{\sqrt{a} - \sqrt{b}}{\sqrt{2}}]^2$.

If the arithmetic and geometric means of $a$ and $b$ are $A$ and $G$ respectively,then the value of $A - G$ is

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