Решите уравнение: (x-2)^2+(x-5)^2=5.

\[(x - 2)^{2} + (x - 5)^{2} = 5\]

\[x^{2} - 4x + 4 + x^{2} - 10x + 25 - 5 = 0\]

\[2x^{2} - 14x + 24 = 0\ \ \ \ \ \ \ \ \ |\ :2\]

\[x^{2} - 7x + 12 = 0\]

\[D = ( - 7)^{2} - 4 \cdot 1 \bullet 12 =\]

\[= 49 - 48 = 1\]

\[x_{1} = \frac{7 + \sqrt{1}}{2} = \frac{7 + 1}{2} = \frac{8}{2} = 4\]

\[x_{2} = \frac{7 - \sqrt{1}}{2} = \frac{7 - 1}{2} = \frac{6}{2} = 3\]

\[Ответ:4;3.\]