Решите уравнение: x^3-3x^2+4x-2=0.

\[x³ - 3x^{2} + 4x - 2 = 0\]

\[P(1) = 1^{3} - 3 \bullet 1^{2} + 4 \bullet 1 - 2 =\]

\[= 1 - 3 + 4 - 2 = 0\]

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

\[x - 1 = 0\]

\[x = 1.\]

\[x² - 2x + 2 = 0\ \]

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

\[= - 4 < 0 \Longrightarrow нет\ решения.\]

\[Ответ:1.\]