ad BĐT bunhiaxopxki có$\left[ (2(x+y)+z(2-xy) \right]^{2}\leq \left[ (x+y)^{2}+z^{2} \right](4+(2-xy)^{2})$
= $(9+2xy)(8+(xy)^{2}-4xy)$
Đăt $t=xy$ ta cần cm $(9+2t)(8+t^{2}-4t)\leq100$
giả sử $\left| x \right| \leq \left| y \right| \leq \left| z\right| \Rightarrow x^{2}\leq y^{2} \leq z^{2}$
$\Rightarrow x^{2}+ y^{2}\leq 6 \Rightarrow xy\leq 3$ hay $t\leq3$
$\Rightarrow đpcm$
dấu "=" $\Leftrightarrow x=-1;y=z=2$