Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Arithmetic mean of a and b = A = $\frac{a+b}{2}$

and geometric mean G = $\sqrt{ab}$

Then A - G = $\frac{a+b}{2}$ - $\sqrt{ab}$ = $\frac{a+b-2\sqrt{ab}}{2}$

= $\frac{(\sqrt{a}{)}^2+(\sqrt{b}{)}^2-2\left(\sqrt{a}\right)\left(\sqrt{b}\right)}{2}$ = $[\frac{\sqrt{a}-\sqrt{b}}{\sqrt{2}}{]}^2$