Для каждого значения a решите систему неравенств: x^2-x-12>0; x>a.

\[\left\{ \begin{matrix} x^{2} - x - 12 > 0 \\ x > a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x^{2} - x - 12 = 0\]

\[x_{1} + x_{2} = 1;\ \ \ \ \ \ x_{1} = 4\]

\[x_{1}x_{2} = - 12;\ \ \ \ \ x_{2} = - 3\]

\[(x + 3)(x - 4) > 0\]

\[x < - 3;\ \ x > 4.\]

\[( - \infty;\ - 3) \cup (4;\ + \infty).\]

\[Если\ a < - 3:\]

\[a < x < - 3\ и\ x > 4.\]

\[Если\ \ \ - 3 \leq a \leq 4:\ \ \ \]

\[x > 4.\]

\[Если\ a > 4:\ \ \ \ \ \]

\[x > a.\]