Рациональные уравнения. Задача 18

ОТВЕТ: \( \pm \sqrt 3 ;\;\;3.\)

\({x^3}-3{x^2}-3x + 9 = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^2}\left( {x-3} \right)-3\left( {x-3} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)

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

Ответ:  \( \pm \sqrt 3 ;\;\;3.\)