Решите уравнение: x^2-6x+7+2/(x^2-6x+10)=0

\[x^{2} - 6x + 7 + \frac{2}{x^{2} - 6x + 10} = 0\]

\[t = x^{2} - 6x + 10;\ \ \ t \neq 0.\]

\[t - 3 + \frac{2}{t} = 0\ \ \ \ \ \ \ \ | \cdot t\]

\[t^{2} - 3t + 2 = 0\]

\[D = ( - 3)^{2} - 4 \cdot 1 \cdot 2 = 9 - 8 =\]

\[= 1;\ \ \ \ \ \sqrt{D} = 1.\]

\[t_{1} = \frac{3 + 1}{2} = \frac{4}{2} = 2;\ \ \]

\[\text{\ \ \ }t_{2} = \frac{3 - 1}{2} = \frac{2}{2} = 1\]

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

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

\[D = ( - 6)^{2} - 4 \cdot 1 \cdot 8 =\]

\[= 36 - 32 = 4;\ \ \ \ \ \ \sqrt{D} = 2.\]

\[x_{1} = \frac{6 + 2}{2} = \frac{8}{2} = 4;\ \ \]

\[\text{\ \ \ }x_{2} = \frac{6 - 2}{2} = \frac{4}{2} = 2\]

\[x^{2} - 6x + 10 = 1\]

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

\[(x - 3)^{2} = 0\]

\[x - 3 = 0\]

\[x = 3\]

\[Ответ:4;2;3.\]