Решебник по алгебре 9 класс Мерзляк Задание 185

\[\boxed{\text{185\ (185).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1) - 3 < x - 4 < 7\]

\[- 3 + 4 < x < 7 + 4\]

\[1 < x < 11\]

\[Ответ:x \in (1;11).\]

\[2) - 2,4 \leq 3x + 0,6 \leq 3\]

\[- 2,4 - 0,6 \leq 3x \leq 3 - 0,6\]

\[- 3 \leq 3x \leq 2,4\]

\[- 3\ :3 \leq x \leq 2,4\ :3\]

\[- 1 \leq x \leq 0,8\]

\[Ответ:x \in \lbrack - 1;0,8\rbrack\]

\[3)\ 0,8 \leq 6 - 2x < 1,4\]

\[0,8 - 6 \leq - 2x < 1,4 - 6\]

\[- 5,2 \leq - 2x < - 4,6\]

\[- 5,2\ :( - 2) \geq x > - 4,6\ :( - 2)\]

\[2,6 \geq x > 2,3\]

\[2,3 < x \leq 2,6\]

\[Ответ:x \in (2,3;2,6\rbrack.\]

\[4)\ 4 < \frac{x}{5} - 2 \leq 5\]

\[4 + 2 < \frac{x}{5} \leq 5 + 2\]

\[6 < \frac{x}{5} \leq 7\]

\[6 \cdot 5 < x \leq 7 \cdot 5\]

\[30 < x \leq 35\]

\[Ответ:x \in (30;35\rbrack\text{.\ }\]

\[\boxed{\text{185.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left\{ \begin{matrix} xy - x = 24 \\ xy - y = 25 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} xy - x - xy + y = - 1 \\ xy - y = 25\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y - x = - 1 \\ xy - y = 25 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = x - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x(x - 1) - x + 1 - 25 = 0 \\ \end{matrix} \right.\ \]

\[x^{2} - x - x + 1 - 25 = 0\]

\[x^{2} - 2x - 24 = 0\]

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

\[x_{1}x_{2} = - 24,\ \ x_{2} = - 4\]

\[\left\{ \begin{matrix} x = 6 \\ y = 5 \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \left\{ \begin{matrix} x = - 4 \\ y = - 5 \\ \end{matrix} \right.\ \]

\[Ответ:(6;5),\ ( - 4;\ - 5).\]

\[2)\ \left\{ \begin{matrix} 2x^{2} + y^{2} = 66 \\ 2x^{2} - y^{2} = 34 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} 2x^{2} + y^{2} - 2x^{2} + y^{2} = 32 \\ 2x^{2} + y^{2} + 2x^{2} - y^{2} = 100 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 2y^{2} = 32 \\ 4x^{2} = 100 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y^{2} = 16 \\ x^{2} = 25 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} y = \pm 4 \\ x = \pm 5 \\ \end{matrix} \right.\ \]

\[Ответ:(5;4),\ (5;\ - 4),\ ( - 5;4),\ \]

\[( - 5;\ - 4)\text{.\ }\]