Решебник по алгебре 9 класс Макарычев Задание 1079

\[\boxed{\text{1079\ (1079).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

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

\[\Longrightarrow \left\{ \begin{matrix} - z^{2} = xy\ \ \ \ \ \ \ \\ (x + y)^{2} = 0\ \ \\ x + y + z = 8 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} - z^{2} = xy \\ x = - y\ \ \\ z = 8\ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} z = 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = - y\ \ \ \ \ \ \ \ \ \ \\ - y \cdot y = - 8^{2} \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} z = 8\ \ \ \ \\ x = - y\ \\ y^{2} = 64 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 8 \\ y = 8\ \ \ \\ z = 8\ \ \ \\ \end{matrix} \right.\ \ \ \ или\ \]

\[\ \left\{ \begin{matrix} x = 8\ \ \ \\ y = - 8 \\ z = 8\ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:( - 8;\ 8;8);\ \ (8;\ - 8;8).\]