$P^2=\frac94x^2+\frac{16}9y^2+\frac{25}{36}z^2+4xy+\frac{20}9yz+\frac52zx$$=(\frac94x^2+\frac14z^2)+(\frac{16}9y^2+\frac49z^2)+4xy+\frac{20}9yz+\frac52zx$
$\ge\frac32xy+\frac{16}9yz+4xy+\frac{20}9yz+\frac52zx$
$=4(xy+yz+zx)=4$
Dấu bằng xảy ra $\begin{cases}z=2y=3x \\ xy+yz+zx=1 \end{cases}$