Решите уравнение x^2+y^2-8x+2y+17=0.

\[x^{2} + y^{2} - 8x + 2y + 17 = 0\]

\[\left( x^{2} - 8x + 16 \right) + \left( y^{2} + 2y + 1 \right) = 0\]

\[(x - 4)^{2} + (y + 1)^{2} = 0\]

\[\left\{ \begin{matrix}
x - 4 = 0 \\
y + 1 = 0 \\
\end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix}
x = 4\ \ \ \\
y = - 1 \\
\end{matrix} \right.\ \]

\[Ответ:(4; - 1).\]