\[\boxed{\text{592\ (592).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[x^{2} - 3x + a = 0;\ \ x_{1}^{2} + x_{2}^{2} = 65\]
\[\left\{ \begin{matrix} \left( x_{1} + x_{2} \right)^{2} = 3^{2} \\ x_{1} \cdot x_{2} = a\ \ \ \ \ \ \ \ \ \\ x_{1}^{2} + x_{2}^{2} = 65\ \ \ \ \ \\ \end{matrix} \right.\ \ \]
\[x_{1}^{2} + 2x_{1}x_{2} + x_{2}^{2} = 9\]
\[\left( x_{1}^{2} + x_{2}^{2} \right) + 2x_{1}x_{2} = 9\]
\[65 + 2a = 9\]
\[2a = - 56\]
\[a = - 28.\]
\[Ответ:a = - 28.\text{\ \ }\]