Решебник по алгебре 9 класс Мерзляк Задание 709

\[\boxed{\mathbf{709\ (709).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ y = \frac{\sqrt{2 - x}}{x + 2}\]

\[\left\{ \begin{matrix} 2 - x \geq 0 \\ x + 2 \neq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x \leq 2\ \ \ \\ x \neq - 2 \\ \end{matrix} \right.\ \]

\[Ответ:x \in ( - \infty;\ - 2) \cup ( - 2;2\rbrack.\]

\[2)\ y = \frac{\sqrt{6 - 5x - x^{2}}}{x - 1}\]

\[\left\{ \begin{matrix} 6 - 5x - x^{2} \geq 0 \\ x - 1 \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} x² + 5x - 6 \leq 0 \\ x \neq 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x^{2} + 5x - 6 = 0\]

\[x_{1} + x_{2} = - 5,\ \ x_{1} = - 6\]

\[x_{1}x_{2} = - 6,\ \ x_{2} = 1\]

\[Ответ:x \in \lbrack - 6;1).\]

\[\boxed{\mathbf{709.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[b_{n} = 10 \cdot 3^{n - 1}\]

\[b_{1} = 10 \cdot 3^{1 - 1} = 10\ \ \]

\[b_{2} = 10 \cdot 3^{2 - 1} = 10 \cdot 3 =\]

\[= 30 \Longrightarrow \ \ q = \frac{30}{10} = 3\]

\[S_{5} = \frac{10 \cdot \left( 3^{5} - 1 \right)}{3 - 1} =\]

\[= \frac{10 \cdot (243 - 1)}{2} =\]

\[= 5 \cdot 242 = 1210.\]

\[Ответ:1210.\]