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Power inequality (Posted on 2005-03-15) Difficulty: 3 of 5
Prove that for all positive x, y, and z,

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

See The Solution Submitted by e.g.    
Rating: 3.0000 (1 votes)

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re: am I wrong ? | Comment 2 of 18 |
(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.

  Posted by Richard on 2005-03-16 00:16:08

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