[tex]x,y\ \textgreater \ 0. \\ \\ x^{3}+ y^{3} \geq x^{2} y+ y^{2}x \\ \Leftrightarrow (x+y)(x^{2}-xy+y^{2}) \geq xy(x+y) \\ \Leftrightarrow x^{2}-xy+y^{2} \geq xy \\ \Leftrightarrow x^{2}-2xy+y^{2} \geq 0 \\ \Leftrightarrow (x-y)^{2} \geq 0, ceea \; ce \; este \; adevarat.[/tex]
