Question

If $\frac{1}{\sqrt{a}}$ is the G.M. of 2 and $\frac{1}{4},$ find a.

Answer 1

$G_1=2$

$G_2=\frac{1}{4}$

$G.M.=\sqrt{G_1{G}_2}$

$G.M.=\sqrt{2\times \frac{1}{4}}$

$G.M.=\frac{1}{\sqrt{2}}$

Comparing with $\frac{1}{\sqrt{a}}$, we get $a=2$.