Решебник по алгебре 9 класс Макарычев Задание 1066

\[\boxed{\text{1066\ (1066).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x_{n} = (n + 4)(n - 5),\]

\[- 18 \leq x_{n} \leq 360.\]

\[(n + 4)(n - 5) \geq - 18\]

\[n^{2} - n - 20 + 18 \geq 0\]

\[n^{2} - n - 2 \geq 0\]

\[(n + 1)(n - 2) \geq 0 \Longrightarrow\]

\[\Longrightarrow n \in ( - \infty; - 1\rbrack \cup \lbrack 2; + \infty).\]

\[(n + 4)(n - 5) \leq 360\]

\[n^{2} - n - 20 - 360 \leq 0\]

\[n^{2} - n - 380 \leq 0\]

\[D = 1 + 4 \cdot 380 = 1521,\]

\[n_{1} = \frac{1 + 39}{2} = 20,\ \ \]

\[n_{2} = \frac{1 - 39}{2} =\]

\[= - 19 \Longrightarrow n \in \lbrack - 19;20\rbrack.\]

\[Ответ:при\ n \in \lbrack 2;20\rbrack.\]