A math problem

Revision en1, by Qualified, 2022-02-07 02:25:13

Prove that for any $$$a, b, c>0$$$ the following inequality is true: \begin{align*} \left(\frac{a^2+b^2+c^2}{3}\right)\left(\frac{b^3}{a}+\frac{c^3}{b}+\frac{a^3}{c}\right) \ \ge a(2b-a)+b(2c-b)+c(2a-c) \end{align*}

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en2 English Qualified 2022-02-07 03:06:06 57
en1 English Qualified 2022-02-07 02:25:13 230 Initial revision (published)