a,b,c>0 and a^4+b^4+c^4 = 3 . Prove the :

sigma\frac{1}{4-ab} =< 1

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- Oct 12th 2005, 07:00 AMmathinequality
a,b,c>0 and a^4+b^4+c^4 = 3 . Prove the :

sigma\frac{1}{4-ab} =< 1 - Nov 12th 2005, 06:42 AMhpeQuote:

Originally Posted by**math**

If and , then

What kind of sum? There is only one term. Or do you mean

?

This inequality appears to be correct. It can probably be proved using Lagrange multipliers: Set and . You want to find the maximum of G subject to F(a,b,c) = 3. The Lagrange equations are

Good luck :)