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МатематикаРешебник по алгебре 9 класс Макарычев Задание 448
Задание 448
\[\boxed{\text{448\ (448).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} - 2y^{2} = 14 \\ x^{2} + 2y^{2} = 18 \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} 2x^{2} = 32\ \ \ \ \ \ \ \ \ \\ 2y^{2} = x^{2} - 14 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x^{2} = 16\ \ \ \ \ \ \ \ \ \\ y^{2} = \frac{x^{2} - 14}{2} \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x_{1} = 4 \\ y_{1} = 1 \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \left\{ \begin{matrix} x_{2} = 4\ \ \\ y_{2} = - 1 \\ \end{matrix} \right.\ \ \ или\]
\[\ \left\{ \begin{matrix} x_{3} = - 4 \\ y_{3} = 1\ \ \ \\ \end{matrix} \right.\ \ \ \ или\mathbf{\text{\ \ \ }}\left\{ \begin{matrix} x_{4} = - 4 \\ y_{4} = - 1 \\ \end{matrix} \right.\ .\]
\[\textbf{б)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 61 \\ x^{2} - y^{2} = 11 \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} 2x^{2} = 72\ \ \ \ \ \ \ \ \\ y^{2} = x^{2} - 11 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x^{2} = 36\ \ \ \ \ \ \ \ \ \ \\ y^{2} = 36 - 11 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x^{2} = 36 \\ y^{2} = 25 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x_{1} = 6 \\ y_{1} = 5 \\ \end{matrix} \right.\ \ \ или\ \ \left\{ \begin{matrix} x_{2} = 6\ \ \ \\ y_{2} = - 5 \\ \end{matrix} \right.\ \ \ или\ \]
\[\ \left\{ \begin{matrix} x_{3} = - 6 \\ y_{3} = 5\ \ \ \ \\ \end{matrix} \right.\ \ \ \ или\ \ \ \left\{ \begin{matrix} x_{4} = - 6 \\ y_{4} = - 5 \\ \end{matrix} \right.\ .\]
\[\textbf{в)}\ \left\{ \begin{matrix} xy + x = 56 \\ xy + y = 54 \\ \end{matrix} \right.\ \ ( - )\]
\[\left\{ \begin{matrix} x - y = 2\ \ \ \ \ \ \ \ \\ y(x + 1) = 54 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = y + 2\ \ \ \ \ \ \\ y(y + 3) = 54 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = y + 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y^{2} + 3y - 54 = 0 \\ \end{matrix} \right.\ \]
\[y^{2} + 3y - 54 = 0\]
\[y_{1} + y_{2} = - 3;\ \ \ y_{1} \cdot y_{2} = - 54\]
\[y_{1} = - 9;\ \ \ y_{2} = 6.\]
\[\Longrightarrow \left\{ \begin{matrix} y_{1} = - 9 \\ x_{1} = - 7 \\ \end{matrix} \right.\ \ \ \ или\ \ \ \left\{ \begin{matrix} y_{2} = 6\ \\ x_{2} = 8. \\ \end{matrix} \right.\ \]
\[Ответ:а)\ (4;1);(4;\ - 1);\]
\[( - 4;1);( - 4;\ - 1);\]
\[\textbf{б)}\ (6;5);(6;\ - 5);\]
\[( - 6;5);( - 6;\ - 5);\]
\[\textbf{в)}\ ( - 7;\ - 9);(8;6).\]
\(\boxed{\text{448.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\)
\[\textbf{а)}\ y > 2x - 3\ \]
\[(5;2);\ \ (0;\ - 5)\text{.\ }\]
\[\textbf{б)}\ y < 3x - 5\]
\[(100;0);\ \ (5;1).\]
\[\textbf{в)}\ y \leq x^{2} - 1\]
\[(1;0);\ \ ( - 1;0).\]
\[\textbf{г)}\ x^{2} + y^{2} \leq 9\ \]
\[(3;3);\ \ (2;1).\]
