15.
[tex]\left\{\begin{matrix} & x^2-xy+y^2=2\geq 2xy-xy & \\ & x^2-xy+y^2=2\geq -2xy-xy & \end{matrix}\right.\\\Leftrightarrow \left\{\begin{matrix} & xy\leq 2 & \\ & xy\geq \frac{-2}{3} & \end{matrix}\right.\\\Leftrightarrow\frac{-2}{3} \leq xy\leq 2[/tex]
[tex]S=x^2+xy+y^2=x^2-xy+y^2+2xy=2+2xy\\2+2.\frac{-2}{3}\leq S=2+2xy\leq 2+2.2\\\Leftrightarrow \frac{2}{3}\leq S\leq 6[/tex]
Chọn A