Найдите целые решения системы неравенств: x^2-(корень из7-2)x-2 корень из7<=0; -x^2+4,8x+1>=0.

\[\left\{ \begin{matrix} x^{2} - \left( \sqrt{7} - 2 \right)x - 2\sqrt{7} \leq 0 \\ - x^{2} + 4,8x + 1 \geq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x^{2} - \left( \sqrt{7} - 2 \right)x - 2\sqrt{7} = 0\]

\[x_{1} + x_{2} = \sqrt{7} - 2\ \ \ \ \ \ \ x_{1} = \sqrt{7}\ \]

\[x_{1}x_{2} = - 2\sqrt{7}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }x_{2} = - 2\]

\[- x^{2} + 4,8x + 1 = 0\]

\[D = 23,04 + 4 = 27,04\]

\[x_{1} = \frac{- 4,8 + 5,2}{- 2} = - 0,2\]

\[x_{2} = \frac{- 4,8 - 5,2}{- 2} = 5\]

\[Ответ:x = 0;\ \ 1;\ \ 2;\ \]