The easiest application of AM - GM

This is one of the easiest application of AM-GM .

We know that , AM $\geq$ GM .

AM of given expression is $\frac{x+\frac{1}{x}}{2}$ and GM of given expression is $1$ .

Hence ; $\frac{x+\frac{1}{x}}{2} \geq 1$ and the result follows .

I.e. $x+\frac{1}{x} \geq 2$ so minimum value of $x+\frac{1}{x}$ is $\boxed {2}$