If a,b,c>0 and a+b+c=3 prove that

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- Aug 6th 2010, 10:34 PMbanku12Inequality 3
If a,b,c>0 and a+b+c=3 prove that

- Aug 16th 2010, 09:40 AMthorin
Hi,

firstly, we can notice that is concave on (by 2 derivations). So, if a,b, and c are in , we can apply the inegality of convexity, and the result is obvious.

Now, if at least one of the 3 numbers is . Then, the 2 others are . Let's say that and and , for example.

Then and and (because has a maxima in and is decreasing on .

finally,

is there a mistake ? - Aug 16th 2010, 11:13 AMAlso sprach Zarathustra
I love your solution!