Решите систему уравнений x+2y=11; xy=14.

Ответ:

\[\left\{ \begin{matrix} x + 2y = 11 \\ xy = 14\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 11 - 2y\ \ \ \ \ \ \ \ \\ (11 - 2y)y = 14 \\ \end{matrix} \right.\ \]

\[11y - 2y^{2} - 14 = 0\]

\[2y^{2} - 11y + 14 = 0\]

\[D = 121 - 112 = 9\]

\[y_{1} = \frac{11 + 3}{4} = \frac{14}{4} = 3,5;\ \ \ \]

\[y_{2} = \frac{11 - 3}{4} = 2.\]

\[\left\{ \begin{matrix} y = 2 \\ x = 7 \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \left\{ \begin{matrix} y = 3,5 \\ x = 4\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(7;2);\ \ (4;3,5).\]