Ta có $x(4-y)(4-z)=x(16-4y-4z+yz)=x(4(x+y+z+\sqrt{xyz})-4y-4z+yz)=x(4x+4\sqrt{xyz}+yz)=x(2\sqrt{x}+\sqrt{yz})^2$$\Rightarrow \sqrt{x(4-y)(4-z)}=2x+\sqrt{xyz}$
tương tự rồi cộng lại
$\Rightarrow P=2x+2y+2z+3\sqrt{xyz}-\sqrt{xyz}=2(x+y+z+\sqrt{xyz})=8$