Рациональные уравнения. Задача 20

ОТВЕТ: -2;  0,5;  2,

\(2{x^3}-{x^2}-8x + 4 = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^2}\left( {2x-1} \right)-4\left( {2x-1} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\,\,\left( {2x-1} \right)\left( {{x^2}-4} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{2x-1 = 0,}\\{{x^2}-4 = 0}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \dfrac{1}{2},\,}\\{x = -2,}\\{x = 2.\,\,\,}\end{array}} \right.\)

Ответ:  –2;  0,5;  2.