Решите уравнение: (x-3)^2+(x-4)^2=5.

\[(x - 3)^{2} + (x - 4)^{2} = 5\]

\[x^{2} - 6x + 9 + x^{2} - 8x + 16 - 5 = 0\]

\[2x^{2} - 14x + 20 = 0\ \ \ \ \ \ \ \ |\ :2\]

\[x^{2} - 7x + 10 = 0\]

\[D = ( - 7)^{2} - 4 \cdot 1 \cdot 10 =\]

\[= 49 - 40 = 9\]

\[x_{1} = \frac{7 + \sqrt{9}}{2} = \frac{7 + 3}{2} = \frac{10}{2} = 5\]

\[x_{2} = \frac{7 - \sqrt{9}}{2} = \frac{7 - 3}{2} = \frac{4}{2} = 2\]

\[Ответ:5;2.\]