We have $$ x_1, x_2,...,x_n \ge 0 $$
and $$ P(n): x_1x_2....x_n \le \left(\frac{x_1+...+x_n}{n}\right)^{n} $$
I have to prove that P(2) is valid.
$$x_1 x_2 \le \left(\frac{x_1+x_2}{2}\right)^{2} $$
I don't know how to achieve this, this is what I tried so far:
$$ \sqrt{x_1x_2} \le \frac{x_1+x_2}{2} $$
$$ 2\sqrt{x_1x_2} \le x_1+x_2 $$
Here, I don't know how to go further. Is this a good way proving this or am I completely wrong?