Prove that for all positive x, y, and z,

(x+y)^z+(y+z)^x+(z+x)^y > 2.

If any of the numbers is greater or equal than 1, the theorem holds.
Say x≥1; then (x+y)^z>1^<>1 and (x+z)^y is also >1.

The problem to be analyzed is when x, y and z are all < 1... that's for later analysis!