Let $x,y,z$ be the non-negative numbers,no two of which are zero.Prove that
$(x^{2}-yz)/(x+y)+(y^{2}-zx)/(y+z)+(z^{2}-xy)/(z+x)>=0$
Inequalities
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- Phlembac Adib Hasan
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Re: Inequalities
Well,it's a direct consequence of Muirhead's inequality.You can also use Holder and Re-arrangement together for easy-looking proofs.Here is a short proof using Cauchy.
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