Prove that for all positive x, y, and z,
(x+y)^z+(y+z)^x+(z+x)^y > 2.
(In reply to
re(2): am I wrong ? by pcbouhid)
I found that when x=y=z~0.183935 that the minimum value is approximately 2.495957862. I believe this is the low value for x=y=z.
I don't think there is a lower value when x, y and z are not equal, but my proof doesn't exist.