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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(2): Can get close to 2 - what is missing ? | Comment 14 of 18 |
(In reply to re: Can get close to 2 - what is missing ? by pcbouhid)

No comment has yet showed that for all positive values of x, y, and z the expression must exceed 2.  Only special cases for the values of x, y, and z have been considered. Being able to get values close to (but larger than) 2, does not prove that a value less than or equal to 2 cannot be achieved. We still need to rule out all values of 2 or less as being values that the expression can take.
  Posted by Richard on 2005-03-27 20:45:15

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