# [Niv2]inégalité

• let $x,y,z$ be positive reals and $m,n,p\geq 2$ be positive integers.

set: $m+n+p=\alpha$

Then show that: $(m+(\frac{\sqrt{xy}}{x+y)})^m)^{\frac{1}{\alpha}}+(n+(\frac{\sqrt{yz}}{y+z})^n)^{\frac{1}{\alpha}}+(p+(\frac{\sqrt{xz}}{x+z)})^p)^{\frac{1}{\alpha}}\geq 3(\frac{3mnp}{64}.2^{\frac{9}{\alpha}})^{\frac{3}{\alpha}}$

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