\[\boxed{\text{589\ (589).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[x^{2} - 12x + q = 0;\ \ \ \ \ \ \ \ \ \ \]
\[x_{1} - x_{2} = 2\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = 12 \\ x_{1}x_{2} = q\ \ \ \ \ \ \ \ \\ x_{1} - x_{2} = 2\ \ \ \\ \end{matrix} \right.\ \ \ \ \ \Longrightarrow \ \ \ x_{1} = 2 + x_{2}\]
\[2 + x_{2} + x_{2} = 12\]
\[2x_{2} = 10\]
\[x_{2} = 5.\]
\[x_{1} = 2 + x_{2} = 2 + 5 = 7.\]
\[q = x_{1}x_{2} = 5 \cdot 7 = 35.\]
\[Ответ:q = 35.\ \]