Найдите целые решения системы неравенств: x^2+(корень из 6-4)x-4корень из 6<=0; -x^2+0,5x+5>=0.

\[\left\{ \begin{matrix} x² + \left( \sqrt{6} - 4 \right)x - 4\sqrt{6} \leq 0 \\ - x^{2} + 0,5x + 5 \geq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x² + \left( \sqrt{6} - 4 \right)x - 4\sqrt{6} = 0\]

\[x_{1} + x_{2} = 4 - \sqrt{6},\]

\[x_{1} \cdot x_{2} = - 4\sqrt{6}\]

\[x_{1} = 4,\ \ x_{2} = - \sqrt{6}\]

\[\left\lbrack - \sqrt{6};4 \right\rbrack.\]

\[- x^{2} + 0,5x + 5 = 0\]

\[x_{1} + x_{2} = 0,5,\ \ x_{1} \cdot x_{2} = - 5\]

\[x_{1} = 2,5,\ \ x_{2} = - 2\]

\[\lbrack - 2;\ - 2,5\rbrack.\]

\[Ответ:\ - 2;\ - 1;0;1;2.\]