|
|
$P^{2}\leq 2\left ( x+\sqrt{2}\times \frac{1}{\sqrt{2}}z \right )^{2}+2\left ( y+\sqrt{2}\times \frac{1}{\sqrt{2}}z \right )^{2}
\leq 6\left ( x^{2}+\frac{z^{2}}{2}+y^{2}+\frac{z^{2}}{2} \right )=18$
$P min=-3\sqrt{2}\Leftrightarrow x=y=\frac{-1}{\sqrt{2}}, z=-\sqrt{2}$
$P max=3\sqrt{2}\Leftrightarrow x=y=\frac{1}{\sqrt{2}}, z=\sqrt{2}$
|