$\leftrightarrow 2y^{2}+2xy+2z^{2}+3x^{2}-2=0 \leftrightarrow (x+y+z)^{2}+y^{2}+z^{2}-2xz-2xy-2+2x^{2}=0\leftrightarrow (x+y+z)^{2}+(x-y)^{2}+(z-x)^{2} -2=0 \leftrightarrow (x+y+z)^{2}\leq 2\rightarrow -\sqrt{2}\leq P\leq \sqrt{2} $dấu bằng xảy ra $\Leftrightarrow x=y=z=\pm \frac{\sqrt{2}}{3}$