Решебник по алгебре 9 класс Мерзляк Задание 164

\[\boxed{\text{164\ (164).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ ax^{2} \leq 0\]

\[x \leq \frac{0}{a^{2}}\]

\[если\ a \neq 0,\ то\ x \leq 0;\]

\[если\ a = 0,\ то\ x - любое\ число.\]

\[2)\ a + x < 2 - ax\]

\[x + ax < 2 - a\]

\[x(1 + a) < 2 - a\]

\[x < \frac{2 - a}{1 + a}\]

\[если\ a > - 1,\ то\ x < \frac{2 - a}{1 + a};\]

\[если\ a < - 1,\ то\ x > \frac{2 - a}{1 + a};\]

\[если\ a = - 1,\ то\ x -\]

\[любое\ число.\]

\[3)\ (a + 4)x > 1\]

\[x > \frac{1}{a + 4}\]

\[если\ a > - 4,\ то\ x > \frac{1}{a + 4};\]

\[если\ a < - 4,\ то\ x < \frac{1}{a + 4};\]

\[если\ a = - 4,\ то\ нет\ решений.\]

\[\boxed{\text{164.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left\{ \begin{matrix} x + y = 5 \\ xy = 6\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

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

\[y = 5 - x\]

\[y = \frac{6}{x}\]

\[Ответ:(2;3);\text{\ \ }(3;2).\]

\[2)\ \left\{ \begin{matrix} x^{2} + y^{2} = 4 \\ x + y = 2\ \ \ \\ \end{matrix}\ \right.\ \text{\ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} x^{2} + y^{2} = 4 \\ y = 2 - x\ \ \ \\ \end{matrix} \right.\ \]

\[x^{2} + y^{2} = 4\]

\[\text{O\ }(0;0)\]

\[r = 2\]

\[y = 2 - x\]

\[\]

\[Ответ:(0;2);\ \ (2;0)\]

\[3)\ \left\{ \begin{matrix} x^{2} + y^{2} = 25 \\ xy = - 12\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} x^{2} + y^{2} = 25 \\ y = - \frac{12}{x}\text{\ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]

\[x^{2} + y^{2} = 25\]

\[\text{O\ }(0;0)\]

\[r = 5\]

\[y = - \frac{12}{x}\ \]

\[Ответ:( - 4;3);\ ( - 3;4);\ \]

\[(4;\ - 3);\ (3;\ - 4).\]

\[4)\ \left\{ \begin{matrix} y = |x|\text{\ \ \ \ \ \ \ } \\ 2y - x = 3 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = |x|\text{\ \ \ \ \ \ \ \ } \\ 2y = x + 3 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = |x|\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ y = 0,5x + 1,5 \\ \end{matrix} \right.\ \]

\[( - 1;1);\ \ (3;3).\]