Решебник по алгебре 9 класс Мерзляк Задание 553

\[\boxed{\mathbf{553\ (553).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \left\{ \begin{matrix} x^{2} + xy + y^{2} = 13 \\ x + y = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} x^{2} + xy + y^{2} = 13 \\ x = 4 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[(4 - y)^{2} + y(4 - y) + y^{2} = 13\]

\[16 - 8y + y^{2} + 4y -\]

\[- y^{2} + y^{2} - 13 = 0\]

\[y² - 4y + 3 = 0\]

\[y_{1} + y_{2} = 4,\ \ y_{1}y_{2} = 3,\ \ \]

\[y = 3,\ \ y = 1\ \]

\[\left\{ \begin{matrix} y = 3 \\ x = 1 \\ \end{matrix}\ \right.\ \ \ \ \ \ или\ \ \ \ \ \ \left\{ \begin{matrix} y = 1 \\ x = 3 \\ \end{matrix} \right.\ \]

\[Ответ:(1;3);\ \ (3;1).\]

\[2)\ \left\{ \begin{matrix} x + xy - y = 13 \\ x - y = 3\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\text{\ \ \ \ \ \ }\left\{ \begin{matrix} x + xy - y = 13 \\ x = 3 + y\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[3 + y + (3 + y)y - y = 13\]

\[3 + y + 3y + y^{2} - y - 13 = 0\]

\[y^{2} + 3y - 10 = 0\]

\[y_{1} + y_{2} = - 3,\ \ \]

\[y_{1}y_{2} = - 10,\ \ \]

\[y = - 5,\ \ y = 2\ \]

\[\left\{ \begin{matrix} y = - 5 \\ x = - 2 \\ \end{matrix}\ \right.\ \ \ \ \ \ или\ \ \ \ \ \ \left\{ \begin{matrix} y = 2 \\ x = 5 \\ \end{matrix} \right.\ \]

\[Ответ:( - 2;\ - 5);\ \ (5;2).\]