AM-GM inequality!



  • Let a1,a2,...,ana_1,a_2,...,a_n be positive real numbers.Prove that
    10(i=1n1ai2+9)j=1naji=1n(j=1,ijnaj2n1)n1410\left ( \sum_{i=1}^{n}\frac{1}{a_i^2+9} \right )\prod_{j=1}^{n}\sqrt{a_j}\leq \sum_{i=1}^{n}\left ( \sum_{j=1,i\neq {j}}^{n}\frac{a_j^2}{n-1} \right )^\frac{n-1}{4}


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