ГДЗ по алгебре 9 класс Макарычев Задание 480

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[Ответ:а)\ (1;1);(4;7);\ \ \ \ \]

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