Решебник по алгебре 9 класс Мерзляк Задание 978

\[\boxed{\mathbf{978\ (978).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \left\{ \begin{matrix} x^{2} - 5x - 6 < 0 \\ x > - 1,2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} (x - 6)(x + 1) < 0 \\ x > - 1,2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:x \in ( - 1;6).\]

\[2)\ \left\{ \begin{matrix} x^{2} - 5x - 6 < 0 \\ x > 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:x \in (0;6).\]

\[3)\ \left\{ \begin{matrix} x^{2} - 5x - 6 < 0 \\ x \geq 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:\ \varnothing.\]

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

\[Ответ:x = 6.\]

\[5)\ \left\{ \begin{matrix} 6x^{2} + x - 2 > 0 \\ x > 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ ,\ \ \]

\[D = 1 + 48 = 49,\ \ \]

\[x = \frac{- 1 + 7}{12} = \frac{1}{2};\ \ \ \ \ \]

\[x = \frac{- 1 - 7}{12} = - \frac{2}{3}\]

\[Ответ:x \in (1;\ + \infty).\]

\[6)\ \left\{ \begin{matrix} 6x^{2} + x - 2 > 0 \\ x > - \frac{1}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]

\[Ответ:x \in (0,5;\ + \infty).\]

\[7)\ \left\{ \begin{matrix} 6x^{2} + x - 2 > 0 \\ x > - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \ \]

\[Ответ:\]

\[x \in \left( - 2;\ - \frac{2}{3} \right) \cup (0,5;\ + \infty).\]

\[8)\ \left\{ \begin{matrix} 6x^{2} + x - 2 \geq 0 \\ x \leq \frac{1}{2}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]

\[Ответ:x \in \left( - \infty;\ - \frac{2}{3} \right) \cup \lbrack 0,5\rbrack.\]