Решите систему неравенств: x^2-x-6>=0; x^2-x-30<0.

Ответ:

\[\left\{ \begin{matrix} x² - x - 6 \geq 0\ \ \ \ \ \ (1) \\ x² - x - 30 < 0\ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1)\ x_{1} + x_{2} = 1,\ \ \ x_{1} \cdot x_{2} = - 6\]

\[x_{1} = 3,\ \ x_{2} = - 2\]

\[(2)\ x_{1} + x_{2} = 1,\ \ \ x_{1} \cdot x_{2} = - 30\]

\[x_{1} = 6,\ \ x_{2} = - 5\]

\[Ответ:( - 5;\ - 2\rbrack \cup \lbrack 3;6).\]