Решите уравнение: x^3-2x^2+3x-2=0.

\[x³ - 2x² + 3x - 2 = 0\]

\[P(1) = 1^{3} - 2 \bullet 1^{2} + 3 \bullet 1 - 2 =\]

\[= 1 - 2 + 3 - 2 = 0\]

\((x - 1)\left( x^{2} - x + 2 \right) = 0\)

\[x - 1 = 0\]

\[x = 1.\]

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

\[D = ( - 1)^{2} - 4 \bullet 1 \bullet 2 =\]

\[= 1 - 8 = - 7 < 0 \Longrightarrow\]

\[\Longrightarrow нет\ решения.\]

\[Ответ:\ \ 1.\]