Backwards induction to show that $x_1\cdots x_n \leq ((x_1+\cdots+x_n)/n )^n$
My question is about backwards induction and was asked previously in the above link. How did they derive the equations for $n=2$, which is $(x_1+x_2)^2−4x_1x_2=(x_1−x_2)^2≥0$
Here's what I have for $n=2$:
$x_1x_2\leq((x_1+x_2)/2)^2$ =$x_1x_2\leq(x_1+x_2)^2/4$
And that's about as far as I get. Can somebody give me any pointers?