Решебник по алгебре 9 класс Макарычев Задание 480

 

\[\boxed{\text{480\ (480).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \left\{ \begin{matrix} y = x^{2} - 3x + 3 \\ 2x - y - 1 = 0\ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 2x - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x - 1 = x^{2} - 3x + 3 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 2x - 1\ \ \ \ \ \ \ \ \ \ \\ x^{2} - 5x + 4 = 0 \\ \end{matrix} \right.\ \]

\[x^{2} - 5x + 4 = 0\]

\[x_{1} + x_{2} = 5;\ \ \ x_{1} \cdot x_{2} = 4\]

\[x_{1} = 4;\ \ \ \ x_{2} = 1.\]

\[\Longrightarrow \left\{ \begin{matrix} x_{1} = 4 \\ y_{1} = 7 \\ \end{matrix} \right.\ \ \ или\ \ \left\{ \begin{matrix} x_{2} = 1 \\ y_{2} = 1. \\ \end{matrix} \right.\ \]

\[\textbf{б)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 100 \\ x + y = 14\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 14 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + (14 - x)^{2} = 100 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 14 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + 196 - 28x + x^{2} = 100 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 14 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x^{2} - 28x + 96 = 0 \\ \end{matrix} \right.\ \]

\[x^{2} - 14x + 48 = 0\]

\[D_{1} = 49 - 48 = 1\]

\[x_{1} = 7 - 1 = 6;x_{2} = 7 + 1 = 8.\]

\[\left\{ \begin{matrix} x_{1} = 6 \\ y_{1} = 8 \\ \end{matrix} \right.\ \ \ \ или\ \ \left\{ \begin{matrix} x_{2} = 8 \\ y_{2} = 6. \\ \end{matrix} \right.\ \ \]

\[Ответ:а)\ (1;1);(4;7);\ \ \ \ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ б)\ \ (6;8);(8;6).\]

\[\boxed{\text{480.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 4x(x + y) + y^{2} = 49 \\ 4x(x - y) + y^{2} = 81 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 4x^{2} + 4xy + y^{2} = 49 \\ 4x^{2} - 4xy + y^{2} = 81 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} (2x + y)^{2} = 49 \\ (2x - y)^{2} = 81 \\ \end{matrix} \right.\ \]

\[1)\ \left\{ \begin{matrix} 2x + y = 7 \\ 2x - y = 9 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 4\ \ \ \ \\ y = - 1 \\ \end{matrix} \right.\ ;\]

\[2)\left\{ \begin{matrix} 2x + y = 7\ \ \\ 2x - y = - 9 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 0,5 \\ y = 8\ \ \ \ \ \\ \end{matrix}; \right.\ \]

\(3)\ \left\{ \begin{matrix} 2x + y = - 7 \\ 2x - y = 9\ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 0,5 \\ y = - 8 \\ \end{matrix} \right.\ ;\ \)

\[4)\ \left\{ \begin{matrix} 2x + y = - 7 \\ 2x - y = - 9 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 4 \\ y = 1.\ \ \\ \end{matrix} \right.\ \]

\[\textbf{б)}\ \left\{ \begin{matrix} 3x(3x - y) + 4y^{2} = 64\ \\ 3x(3x + 4y) + 4y^{2} = 16 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 9x^{2} - 12xy + 4y^{2} = 64 \\ 9x^{2} + 12xy + 4y^{2} = 16 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} (3x - 2y)^{2} = 64 \\ (3x + 2y)^{2} = 16 \\ \end{matrix} \right.\ \]

\[1)\ \left\{ \begin{matrix} 3x - 2y = 8 \\ 3x + 2y = 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 2\ \ \ \\ y = - 1 \\ \end{matrix} \right.\ ;\]

\[2)\ \left\{ \begin{matrix} 3x - 2y = 8\ \ \\ 3x + 2y = - 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = \frac{2}{3}\text{\ \ } \\ y = - 3 \\ \end{matrix} \right.\ ;\]

\[3)\ \left\{ \begin{matrix} 3x - 2y = - 8 \\ 3x + 2y = 4\ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - \frac{2}{3} \\ y = 3\ \ \ \\ \end{matrix} \right.\ ;\]

\[4)\ \left\{ \begin{matrix} 3x - 2y = - 8 \\ 3x + 2y = - 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 2 \\ y = 1.\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:а)\ (4;\ - 1);\ \ ( - 4;1);\ \]

\[\ (0,5;\ - 8);( - 0,5;8);\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ б)\ (2;\ - 1);( - 2;1);\]

\[\left( \frac{2}{3};\ - 3 \right);\left( - \frac{2}{3};3 \right).\]