Решите систему неравенств: 2x^2+11x-6<=0; x^2+8x<=0.

Ответ:

\[\left\{ \begin{matrix} 2x² + 11x - 6 \leq 0 \\ x² + 8x \leq 0\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[2x^{2} + 11x - 6 = 0\]

\[D = 121 + 48 = 169\]

\[x_{1} = \frac{- 11 + 13}{4} = 0,5\]

\[x_{2} = \frac{- 11 - 13}{4} = - 6\]

\[\lbrack - 6;0,5\rbrack.\]

\[x(x + 8) = 0\]

\[x = 0,\ \ x = - 8\]

\[\lbrack - 8;0\rbrack.\]

\[Ответ:\lbrack - 6;0\rbrack.\]