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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 164
Задание 164
\[\boxed{\text{164\ (164).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ ax^{2} \leq 0\]
\[x \leq \frac{0}{a^{2}}\]
\[если\ a \neq 0,\ то\ x \leq 0;\]
\[если\ a = 0,\ то\ x - любое\ число.\]
\[2)\ a + x < 2 - ax\]
\[x + ax < 2 - a\]
\[x(1 + a) < 2 - a\]
\[x < \frac{2 - a}{1 + a}\]
\[если\ a > - 1,\ то\ x < \frac{2 - a}{1 + a};\]
\[если\ a < - 1,\ то\ x > \frac{2 - a}{1 + a};\]
\[если\ a = - 1,\ то\ x -\]
\[любое\ число.\]
\[3)\ (a + 4)x > 1\]
\[x > \frac{1}{a + 4}\]
\[если\ a > - 4,\ то\ x > \frac{1}{a + 4};\]
\[если\ a < - 4,\ то\ x < \frac{1}{a + 4};\]
\[если\ a = - 4,\ то\ нет\ решений.\]
\[\boxed{\text{164.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \left\{ \begin{matrix} x + y = 5 \\ xy = 6\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} y = 5 - x \\ y = \frac{6}{x}\text{\ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]
\[y = 5 - x\]
| \[x\] | \[1\] | \[2\] |
|---|---|---|
| \[y\] | \[4\] | \[3\] |
\[y = \frac{6}{x}\]
| \[x\] | \[1\] | \[2\] | \[3\] | \[6\] | \[- 1\] | \[- 2\] | \[- 3\] | \[- 6\] |
|---|---|---|---|---|---|---|---|---|
| \[y\] | \[6\] | \[3\] | \[2\] | \[1\] | \[- 6\] | \[- 3\] | \[- 2\] | \[- 1\] |
\[Ответ:(2;3);\text{\ \ }(3;2).\]
\[2)\ \left\{ \begin{matrix} x^{2} + y^{2} = 4 \\ x + y = 2\ \ \ \\ \end{matrix}\ \right.\ \text{\ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} x^{2} + y^{2} = 4 \\ y = 2 - x\ \ \ \\ \end{matrix} \right.\ \]
\[x^{2} + y^{2} = 4\]
\[\text{O\ }(0;0)\]
\[r = 2\]
\[y = 2 - x\]
| \[x\] | \[0\] | \[1\] |
|---|---|---|
| \[y\] | \[2\] | \[1\] |
\[\]
\[Ответ:(0;2);\ \ (2;0)\]
\[3)\ \left\{ \begin{matrix} x^{2} + y^{2} = 25 \\ xy = - 12\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]
\[\text{\ \ }\left\{ \begin{matrix} x^{2} + y^{2} = 25 \\ y = - \frac{12}{x}\text{\ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]
\[x^{2} + y^{2} = 25\]
\[\text{O\ }(0;0)\]
\[r = 5\]
\[y = - \frac{12}{x}\ \]
| \[x\] | \[2\] | \[6\] | \[1\] | \[12\] | \[- 2\] | \[- 6\] | \[- 1\] | \[- 12\] |
|---|---|---|---|---|---|---|---|---|
| \[y\] | \[- 6\] | \[- 2\] | \[- 12\] | \[- 1\] | \[6\] | \[2\] | \[12\] | \[1\] |
\[Ответ:( - 4;3);\ ( - 3;4);\ \]
\[(4;\ - 3);\ (3;\ - 4).\]
\[4)\ \left\{ \begin{matrix} y = |x|\text{\ \ \ \ \ \ \ } \\ 2y - x = 3 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = |x|\text{\ \ \ \ \ \ \ \ } \\ 2y = x + 3 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = |x|\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ y = 0,5x + 1,5 \\ \end{matrix} \right.\ \]
\[( - 1;1);\ \ (3;3).\]
