Решите уравнение: |x^2-3x+2|=|x^2-2x+3|.

\[\left| x^{2} - 3x + 2 \right| = \left| x^{2} - 2x + 3 \right|\]

\[- 2x + 3x = 2 - 3\]

\[x = \text{-}1.\]

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

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

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

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

\[D = ( - 5)^{2} - 4 \cdot 2 \cdot 5 =\]

\[= 25 - 40 = - 15 < 0 -\]

\[нет\ решения.\]

\[Ответ:\ - 1.\]