1. ## Inequality

Could someone please explain how to solve this problem. Cheers troops.

2. $\begin{gathered}
\left( {a - b} \right)^2 \geqslant 0 \Rightarrow \quad a^2 + b^2 \geqslant 2ab \hfill \\
\text{let }a = \sqrt x \,\& \,b = \frac{1}
{{\sqrt x }} \hfill \\
\end{gathered}$

3. And since you're in calculus, you can also differentiate the function $f(x)=x+\frac 1x$
and see its variations