Решите уравнение: x^4-2x^3+2x-1=0.

\[x^{4} - 2x^{3} + 2x - 1 = 0\]

\[\left( x^{4} - 1 \right) - \left( 2x^{3} - 2x \right) = 0\]

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

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

\[1)\ x^{2} - 1 = 0\]

\[x^{2} = 1\]

\[x = \pm 1.\]

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

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

\[x - 1 = 0\]

\[x = 1.\]

\[Ответ:x = \pm 1.\]