Задача 20. Решите уравнение \(2{x^3}-{x^2}-8x + 4 = 0\)
ОТВЕТ: -2; 0,5; 2,Ответ
\(2{x^3}-{x^2}-8x + 4 = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^2}\left( {2x-1} \right)-4\left( {2x-1} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,\left( {2x-1} \right)\left( {{x^2}-4} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{2x-1 = 0,}\\{{x^2}-4 = 0}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \frac{1}{2},\,}\\{x = -2,}\\{x = 2.\,\,\,}\end{array}} \right.\) Ответ: –2; 0,5; 2.Решение