Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаРешебник по алгебре 9 класс Макарычев Задание 529
Задание 529
\[\boxed{\text{529}\text{\ (529)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 40 \\ xy = - 12\ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x^{2} + 2xy + y^{2} = 40 - 24 \\ 2xy = - 24\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} (x + y)^{2} = 16 \\ xy = - 12\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x + y = 4 \\ xy = - 12 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = 4 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y(4 - y) + 12 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = 4 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \\ y^{2} - 4y - 12 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y_{1} = 6\ \ \ \\ x_{1} = - 2 \\ \end{matrix} \right.\ \ \ или\ \left\{ \begin{matrix} y_{2} = - 2 \\ x_{2} = 6.\ \ \\ \end{matrix} \right.\ \]
\[2)\ \left\{ \begin{matrix} x + y = - 4 \\ xy = - 12\ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = - 4 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ ( - 4 - y) \cdot y = - 12 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = - 4 - y\ \ \ \ \ \ \ \ \ \\ y^{2} + 4y - 12 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y_{1} = - 6 \\ x_{1} = 2\ \ \ \\ \end{matrix} \right.\ \ \ \ \ или\ \left\{ \begin{matrix} y_{2} = 2\ \ \ \\ x_{2} = - 6. \\ \end{matrix} \right.\ \ \]
\[\textbf{б)}\ \left\{ \begin{matrix} x^{2} + 2y^{2} = 228\ \ \ \\ 3x^{2} - 2y^{2} = 172 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 4x^{2} = 228 + 172 \\ 2y^{2} = 228 - x^{2}\text{\ \ } \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x² = 100 \\ y² = 64\ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = \pm 10 \\ y = \pm 8.\ \ \\ \end{matrix} \right.\ \]
\[Ответ:а)\ ( - 2;6);(6;\ - 2);\ \ \ \]
\[\textbf{б)}\ (10;8);( - 10;\ - 8);(10;\ - 8);\]
\[( - 10;8).\]
\[\boxed{\text{529.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ x_{32},x_{33},x_{34};\]
\[\textbf{б)}\ x_{n + 1},\ x_{n + 2},\ x_{n + 3},\ x_{n + 4},\ x_{n + 5};\]
\[\textbf{в)}\ x_{n - 3},\ x_{n - 2},\ x_{n - 1};\]
\[\textbf{г)}\ x_{n - 1},\ x_{n},\ x_{n + 1}.\]
