Ta thấy: [tex]x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)\geq (y+z-2x)[x^2+\frac{y^2+z^2+2yz}{4}-xy-yz-zx+\frac{3}{4}(y^2+z^2-2yz)]=2(\frac{y+z}{2}-x)[(\frac{y+z}{2}-x)^2+\frac{3}{4}(y-z)^2]\geq 2(\frac{y+z}{2}-x)(\frac{y+z}{2}-x)^2=2(\frac{y+z}{2}-x)^3(đpcm)[/tex]
