perplexus.info :: Just Math : Power inequality

Power inequality (Posted on 2005-03-15)

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): am I wrong ?

| Comment 4 of 18 |

(In reply to re: am I wrong ? by Richard)

Richard,

I discover that this sum has a POINT OF INFLEXION, near to 2.5, for z = 0,183.......... I don't know what represents this number.

You could see it using Excel.

My mistake is the conclusion that the sum is >=3. But it is indeed greater than 2.

Posted by pcbouhid on 2005-03-16 13:07:28

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