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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(4): Can get close to 2 - what is missing ? | Comment 16 of 18 |
(In reply to re(3): Can get close to 2 - what is missing ? by pcbouhid)

Two or three of the variables being equal is not general enough. In all of the instances you mention that involve small values or values slightly less than 1, two or three of x, y, and z are always equal.  If you have pertinent modifications of the "e, 1-e" results, you need to write them out in detail and show how they give a proof for general values of x, y, and z no two of which are equal. Consideration may however be limited to values of x, y, and z that are between 0 and 1, since if any is 1 or greater, the result is clearly true.
  Posted by Richard on 2005-03-28 03:45:01

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