Question Number 158276 by HongKing last updated on 01/Nov/21
$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{then}: \\ $$$$\mathrm{2}\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\:\geqslant\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\mathrm{x}\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \right)\:+\:\mathrm{xyz}\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right) \\ $$$$ \\ $$