Решите уравнение: |x^2-5x+2|=|x^2+6x-5|.

\[\left| x^{2} - 5x + 2 \right| = \left| x^{2} + 6x - 5 \right|\]

\[x^{2} - 5x + 2 = x^{2} + 6x - 5\]

\[6x + 5x = 2 + 5\]

\[11x = 7\]

\[x = \frac{7}{11}.\]

\[x^{2} - 5x + 2 = - \left( x^{2} + 6x - 5 \right)\]

\[x^{2} - 5x + 2 = - x^{2} - 6x + 5\]

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

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

\[D = 1^{2} - 4 \cdot 2 \cdot ( - 3) = 1 + 24 =\]

\[= 25\]

\[x_{1} = \frac{- 1 + \sqrt{25}}{4} = \frac{- 1 + 5}{4} = \frac{4}{4} =\]

\[= 1\]

\[x_{2} = \frac{- 1 - \sqrt{25}}{4} = \frac{- 1 - 5}{4} =\]

\[= \frac{- 6}{4} = - 1\frac{2}{4} = - 1\frac{1}{2} = - 1,5.\]

\[Ответ:\ \frac{7}{11};\ \ 1;\ - 1,5.\]