\[\boxed{\mathbf{725\ (725).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[x^{2} - 10x + c = 0\]
\[x_{1}\text{\ \ }и\ \ \ x_{2},\ \ \]
\[причем\ \ x_{2} = x_{1} + 8\]
\[x_{1} + x_{2} = 10\]
\[x_{1} + x_{1} + 8 = 10\]
\[2x_{1} = 2\]
\[x_{1} = 1\]
\[x_{2} = 10 - 1 = 9\]
\[x_{1} \cdot x_{2} = c\]
\[1 \cdot 9 = 9\]
\[Ответ:\ x_{1} = 1;\ \ x_{2} = 9;\ \ \ \ \ c = 9.\]