Q:

Showing the inequality is true or false given the conditions

I know:
$|2xy|<x^2+y^2$
Is it possible to show using this that $xy>x+y$ where $x,y$ $\in$ $\{3,4,5,6...\}$.
Sorry I do not know how to write positive integer minus $1,2$
I am try to solve the inequality so I started off using 
$|2xy|<x^2+y^2$
and dividing by 2
$|xy|<\frac{x^2+y^2}{2}$
but i stuck from there on. I try to look for examples that do not work but i dont find any.

A:

$$x>2\space,\quad y>2$$
$$\frac 1x<\frac12\space,\quad \frac 1y<\frac12$$
$$\frac 1x + \frac 1y < 1$$
$$xy\left(\frac 1x + \frac 1y\right) < xy$$
$$ x + y < xy$$

