Question

Find $x$, if $\sqrt{2},x,\frac{1}{\sqrt{2}}$ are in G.P.

Answer 1

We know that the geometric mean between two numbers $a$ and $b$ is $GM=\sqrt{ab}$.

Here, it is given that $GM=x$, $a=\sqrt{2}$ and $b=\frac{1}{\sqrt{2}}$, therefore,

$GM=\sqrt{ab}\Rightarrow x=\sqrt{\sqrt{2}\times \frac{1}{\sqrt{2}}}\Rightarrow x=\sqrt{1}\Rightarrow x=1$

Hence, $x=1$