A) \[\frac{a-b}{a}\]
B) \[\frac{a+b}{2}\]
C) \[{{\left[ \frac{\sqrt{a}-\sqrt{b}}{\sqrt{2}} \right]}^{2}}\]
D) \[\frac{2ab}{a+b}\]
Correct Answer: C
Solution :
Arithmetic mean of \[a\] and \[b=A=\frac{a+b}{2}\] and geometric mean \[G=\sqrt{ab}\] Then \[A-G=\frac{a+b}{2}-\sqrt{ab}\]\[=\frac{a+b-2\sqrt{ab}}{2}\] \[=\frac{{{(\sqrt{a})}^{2}}+{{(\sqrt{b})}^{2}}-2(\sqrt{a})(\sqrt{b})}{2}={{\left[ \frac{\sqrt{a}-\sqrt{b}}{\sqrt{2}} \right]}^{2}}\]
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