\(Q=\Sigma\frac{x^2}{xy^2z}+\frac{x^5}{y}+\frac{y^5}{z}+\frac{z^5}{x}\ge\frac{\left(x+y+z\right)^2}{xyz\left(x+y+z\right)}+4\sqrt[4]{\frac{x^5y^5z^5}{xyz}.\frac{1}{16}}-\frac{1}{16}\)
\(=\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}+2xyz-\frac{1}{16}=\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}+32xyz+32xyz-62xyz-\frac{1}{16}\)
\(\ge5\sqrt[5]{\frac{1}{\left(xyz\right)^2}.32^2\left(xyz\right)^2}-\frac{62}{27}\left(x+y+z\right)^3-\frac{1}{16}=20-\frac{31}{4}-\frac{1}{16}=\frac{195}{16}\)
Dấu "=" xảy ra khi \(x=y=z=\frac{1}{2}\)
