\(\frac{x}{yz}+\frac{y}{zx}+\frac{z}{xy}\ge\sqrt{\frac{xy}{yz.zx}}+\sqrt{\frac{xz}{yz.xy}}+\sqrt{\frac{yz}{zx.xy}}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\)
\(\Rightarrow P\ge\frac{1}{2}\left(x^2+y^2+z^2\right)+\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\)
\(P\ge\frac{1}{6}\left(x+y+z\right)^2+\frac{9}{x+y+z}=\frac{1}{6}\left(x+y+z\right)^2+\frac{9}{2\left(x+y+z\right)}+\frac{9}{2\left(x+y+z\right)}\)
\(P\ge3\sqrt[3]{\frac{81\left(x+y+z\right)^2}{24\left(x+y+z\right)^2}}=\frac{9}{2}\)
Dấu "=" xảy ra khi \(x=y=z=1\)
