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

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

If we allow the  formula to include zero values for the three variables (except for all three equal to zero), then the differentiable function defined thereby will attain its minimum of 2 on the three axes, I conjecture.

Posted by Richard on 2005-03-17 01:00:11