Решите систему уравнений: x+y=7; xy=12.

Ответ:

\[\left\{ \begin{matrix} x + y = 7 \\ xy = 12\ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} y = 7 - x\ \ \ \ \ \ \ \ \\ x(7 - x) = 12 \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} y = 7 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 7x - x^{2} - 12 = 0 \\ \end{matrix} \right.\ \]

\[- x^{2} + 7x - 12 = 0\]

\[x_{1} + x_{2} = 7\ \ \ \ \ \ \ x_{1} = 3\]

\[x_{1}x_{2} = 12\ \ \ \ \ \ \ \ \ \ x_{2} = 4\ \]

\[\left\{ \begin{matrix} x = 3 \\ y = 4 \\ \end{matrix}\ \ \ \ \ \ \ или\ \ \right.\ \text{\ \ \ }\left\{ \begin{matrix} x = 4 \\ y = 3 \\ \end{matrix} \right.\ \]

\[Ответ:(3;4),\ (4;\ \ 3)\text{.\ }\]