[Niv2]inégalité


  • Math&Maroc

    let x,y,zx,y,z be positive reals and m,n,p2m,n,p\geq 2 be positive integers.

    set: m+n+p=αm+n+p=\alpha

    Then show that: (m+(xyx+y))m)1α+(n+(yzy+z)n)1α+(p+(xzx+z))p)1α3(3mnp64.29α)3α(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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