Prove that for all positive x, y, and z,
(x+y)^z+(y+z)^x+(z+x)^y > 2.
(In reply to
am I wrong ? by pcbouhid)
Yes, you are wrong. Let x=1/2, y=1/4, and z=1/8. Then S=
2.466190771 and 3*(2z)^z=2.522689246 (which is less than 3, also).
Your inequality has problems when the values are less than 1, since (1/2)^(1/4) > (1/2)^(1/2) for example.
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Posted by Richard
on 2005-03-16 00:16:08 |