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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 449
Задание 449
\[\boxed{\text{449\ (449).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \left\{ \begin{matrix} x + y = 5 \\ xy = 6\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 5 - x \\ y = \frac{6}{x}\text{\ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]
\[y = 5 - x\]
| \[x\] | \[1\] | \[2\] |
|---|---|---|
| \[y\] | \[4\] | \[3\] |
\[y = \frac{6}{x}\]
| \[x\] | \[1\] | \[2\] | \[3\] | \[6\] | \[- 1\] | \[- 2\] | \[- 3\] | \[- 6\] |
|---|---|---|---|---|---|---|---|---|
| \[y\] | \[6\] | \[3\] | \[2\] | \[1\] | \[- 6\] | \[- 3\] | \[- 2\] | \[- 1\] |
\[Ответ:(2;3);\text{\ \ }(3;2).\]
\[2)\ \left\{ \begin{matrix} y + x^{2} = 3 \\ y = x - 1\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 3 - x^{2} \\ y = x - 1\ \ \\ \end{matrix} \right.\ \]
\[y = 3 - x^{2}\]
\[график\ функции\ y = - x^{2}\ \]
\[поднять\ на\ 3\ единицы\ ввепх.\]
\[y = x - 1\]
| \[x\] | \[0\] | \[1\] |
|---|---|---|
| \[y\] | \[- 1\] | \[0\] |
\[Ответ:( \approx - 2,5;\ - 3,5);\ \ \]
\[( \approx 1,5;\ \approx 0,6).\]
\[3)\ \left\{ \begin{matrix} x^{2} + y^{2} = 4 \\ x + y = 2\ \ \ \\ \end{matrix}\ \right.\ \text{\ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} x^{2} + y^{2} = 4 \\ y = 2 - x\ \ \ \\ \end{matrix} \right.\ \]
\[x^{2} + y^{2} = 4\]
\[\text{O\ }(0;0)\]
\[r = 2\]
\[y = 2 - x\]
| \[x\] | \[0\] | \[1\] |
|---|---|---|
| \[y\] | \[2\] | \[1\] |
\[\]
\[Ответ:(0;2);\ \ (2;0)\]
\[4)\ \left\{ \begin{matrix} x^{2} + y^{2} = 25 \\ xy = - 12\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]
\[\text{\ \ }\left\{ \begin{matrix} x^{2} + y^{2} = 25 \\ y = - \frac{12}{x}\text{\ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]
\[x^{2} + y^{2} = 25\]
\[\text{O\ }(0;0)\]
\[r = 5\]
\[y = - \frac{12}{x}\ \]
| \[x\] | \[2\] | \[6\] | \[1\] | \[12\] | \[- 2\] | \[- 6\] | \[- 1\] | \[- 12\] |
|---|---|---|---|---|---|---|---|---|
| \[y\] | \[- 6\] | \[- 2\] | \[- 12\] | \[- 1\] | \[6\] | \[2\] | \[12\] | \[1\] |
\[Ответ:( - 4;3);\ ( - 3;4);\ \]
\[(4;\ - 3);\ (3;\ - 4).\]
