ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 709

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\[\left\{ \begin{matrix} y = 0,5x^{2} - 2 \\ y - x = 2\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

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

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

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

\[\Longrightarrow \left\{ \begin{matrix} y = x + 2\ \ \ \ \ \ \ \ \ \ \ \\ x² - 2x - 8 = 0 \\ \end{matrix} \right.\ \]

\[x^{2} - 2x - 8 = 0\]

\[D_{1} = 1 + 8 = 9\]

\[x_{1} = 1 + 3 = 4;\ \ \ \]

\[x - 2 = 1 - 3 = - 2.\]

\[1)\ x_{1} = 4;\ \ \ \ \ \ \ \ y_{1} = 6;\]

\[2)\ x_{2} = - 2;\ \ \ \ y_{2} = 0.\]

\[Ответ:(4;6);\ \ ( - 2;0).\]