\[\boxed{\text{683\ (683).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x^{2} + px + q = 0,\ \ x_{1}^{2} + x_{2}^{2} - ?\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = - p \\ x_{1}x_{2} = q\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[x_{1}^{2} + x_{2}^{2} =\]
\[= x_{1}^{2} + 2x_{1}x_{2} + x_{2}^{2} - 2x_{1}x_{2} =\]
\[= \left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2} =\]
\[= ( - p)^{2} - 2q = p^{2} - 2q\]
\[Ответ:p^{2} - 2q.\ \]