Простейшие иррациональные уравнения. Задача 14

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\(\sqrt[3]{{{x^3}-3x-1}} = x-1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^3}-3x-1 = {x^3}-3{x^2} + 3x-1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,3{x^2}-6x = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\)

\( \Leftrightarrow \,\,\,\,\,\,\,x\left( {3x-6} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,\,\,\,}\\{3x-6 = 0}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,}\\{x = 2.}\end{array}} \right.\)

Ответ:  0; 2.