Решите уравнение: (x-5)^2+(x-3)^2=2.

\[(x - 5)^{2} + (x - 3)^{2} = 2\]

\[x^{2} - 10x + 25 + x^{2} - 6x + 9 - 2 = 0\]

\[2x^{2} - 16x + 32 = 0\ \ \ \ \ \ \ \ |\ :2\]

\[x^{2} - 8x + 16 = 0\]

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

\[x - 4 = 0\]

\[x = 4\]

\[Ответ:x = 4.\]