Решебник по алгебре 9 класс Мерзляк Задание 218

\[\boxed{\text{218\ (218).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[3x^{2} - (2a + 5)x + 2 +\]

\[+ a - a^{2} = 0\ \ \]

\[\left\{ \begin{matrix} x_{1} < - 2 \\ x_{2} > 3\ \ \ \\ \end{matrix} \right.\ \text{\ \ }или\ \ \left\{ \begin{matrix} x_{2} < - 2 \\ x_{1} > 3\ \ \ \\ \end{matrix} \right.\ \]

\[D = (2a + 5)^{2} -\]

\[- 12 \cdot \left( 2 + a - a^{2} \right) =\]

\[= 4a^{2} + 20a + 25 - 24 -\]

\[- 12a + 12a^{2} =\]

\[= 16a^{2} + 8a + 1 = (4a + 1)^{2}.\]

\[x_{1} = \frac{2a + 5 + 4a + 1}{6} =\]

\[= \frac{6a + 6}{6} = a + 1\]

\[x_{2} = \frac{2a + 5 - 4a - 1}{6} =\]

\[= \frac{- 2a + 4}{6} = \frac{- a + 2}{3}\]

\[1)\ \left\{ \begin{matrix} a + 1 < - 2 \\ \frac{- a + 2}{3} > 3\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} a < - 3\ \ \ \ \ \ \ \ \\ - a + 2 > 9 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} a < - 3 \\ - a > 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} a < - 3 \\ a < - 7 \\ \end{matrix} \right.\ \]

\[\ a \in ( - \infty;\ - 7).\]

\[2)\ \left\{ \begin{matrix} a + 1 > 3\ \ \ \ \ \ \ \\ \frac{- a + 2}{3} < - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} a > 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - a + 2 < - 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} a > 2\ \ \ \ \ \ \ \ \\ - a < - 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} a > 2 \\ a > 8 \\ \end{matrix} \right.\ \]

\(\text{\ \ \ \ \ \ \ \ \ \ }\)

\[a \in (8;\ + \infty).\]

\[Ответ:a \in ( - \infty;\ - 7) \cup (8;\ + \infty)\text{.\ }\]