Решебник по алгебре 9 класс Мерзляк Задание 987

\[\boxed{\mathbf{987\ (987).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\left\{ \begin{matrix} x - y = 2 \\ xy = a\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = y + 2\ \ \ \ \ \\ y(y + 2) = a \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

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

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

\[D = 1 + a = 0\]

\[a = - 1\]

\[Ответ:\ a = - 1.\]

\[2)\ \left\{ \begin{matrix} x^{2} + y^{2} = 6 \\ x + y = a\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} (a - y)^{2} + y^{2} = 6 \\ x = a - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[a^{2} - 2ay + y^{2} + y^{2} - 6 = 0\]

\[2y^{2} - 2ay + a^{2} - 6 = 0\]

\[D = 4a^{2} - 8 \cdot \left( a^{2} - 6 \right) = 4a^{2} -\]

\[- 8a^{2} + 48 = 48 - 4a^{2} = 0\]

\[4a^{2} = 48,\ \ a^{2} = 12,\]

\[\text{\ \ a} = \pm 2\sqrt{3}\]

\[Ответ:\text{\ a} = \pm 2\sqrt{3}\text{.\ }\]