If A and G are the arithmetic mean and geomet | vedclass

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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 $G = \sqrt{ab}$.Therefore,$A - G = \frac{a + b}{2

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

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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 $G = \sqrt{ab}$.Therefore,$A - G = \frac{a + b}{2} - \sqrt{ab}$.$A - G = \frac{a + b - 2\sqrt{ab}}{2}$.Since $a = (\sqrt{a})^2$ and $b = (\sqrt{b})^2$,we have $A - G = \frac{(\sqrt{a})^2 + (\sqrt{b})^2 - 2\sqrt{a}\sqrt{b}}{2}$.$A - G = \frac{(\sqrt{a} - \sqrt{b})^2}{2} = \left[ \frac{\sqrt{a} - \sqrt{b}}{\sqrt{2}} \right]^2$.

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

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