How was this simplified?

Question

How can $\sqrt{e^{2x}+e^{-2x}+2}\ $ be simplified to yield $e^x+e^{-x}$?

I don't understand the steps that were taken to get to that, I'm really confused to how they are equivalent.

Thanks for your help.

Answer 1

$$(e^x)^2+(e^{-x})^2+2e^x\cdot e^{-x}=?$$

and $$e^x+e^{-x}\ge2\sqrt{e^x\cdot e^{-x}}>0$$

$$\sqrt{a^2}=|a|=+a$$ for real $a\ge0$

Answer 2

HINT

Note that

$$(e^x+e^{-x})^2=e^{2x}+e^{-2x}+2$$

and

$$e^x+e^{-x}>0$$