If the arithmetic and geometric means of a an | vedclass

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Question

(c) Arithmetic mean of $a$ and $b = A = \frac{{a + b}}{2}$

and geometric mean $G = \sqrt {ab} $

Then $A - G = \frac{{a + b}}{2} - \sqrt {ab} $$

Vedclass · Accepted Answer

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

Vedclass · Answer

(c) Arithmetic mean of $a$ and $b = A = \frac{{a + b}}{2}$

and geometric mean $G = \sqrt {ab} $

Then $A - G = \frac{{a + b}}{2} - \sqrt {ab} $$ = \frac{{a + b - 2\sqrt {ab} }}{2}$

$ = \frac{{{{(\sqrt a )}^2} + {{(\sqrt b )}^2} - 2(\sqrt a )(\sqrt b )}}{2} = {\left[ {\frac{{\sqrt a - \sqrt b }}{{\sqrt 2 }}} \right]^2}$

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

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