Решите уравнение: |x-2|(x^2-4x+2)=2*(x-2).

\[|x - 2|\left( x^{2} - 4x + 2 \right) =\]

\[= 2 \bullet (x - 2)\]

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

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

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

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

\[x - 2 = 0\]

\[x = 2 \Longrightarrow \ \ \ не\ подходит.\]

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

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

\[(x - 2) \bullet x \bullet (x - 4) = 0\]

\[x = 0 \Longrightarrow \ \ не\ подходит.\]

\[x = 2;\ \ \ x = 4\]

\[Ответ:2;4.\]