[Unsolved] inegalité



  • Let a,b,c1a,b,c \geq 1 , prove that :
    cycab5+b23×(ab+bc+ac)2\sum_{cyc} a\sqrt{b^5+\sqrt{b}} \geq \frac{\sqrt{2}}{3} \times (\sqrt{ab}+\sqrt{bc}+\sqrt{ac})^2


  • Math&Maroc

    @Amine-medrare b5+b2b1142b2b^5+\sqrt{b}\geq 2b^{\frac{11}{4}}\geq 2b^2, car b1b\geq 1.
    D.ou L.H.S2(ab+bc+ca)R.H.SL.H.S\geq \sqrt{2}(ab+bc+ca)\geq R.H.S.
    La derniere inegalite est une application de Cauchy-Schwarz. Egalite a lieu si a=b=c=1a=b=c=1.


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