Задача 16. Решите уравнение \({x^3}-3{x^2} = 4x\)
ОТВЕТ: -1; 0; 4.Ответ
\({x^3}-3{x^2} = 4x\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^3}-3{x^2}-4x = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\left( {{x^2}-3x-4} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\\{{x^2}-3x-4 = 0}\end{array}} \right.\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,}\\{x = -1,}\\{x = 4.\,\,}\end{array}} \right.\) Ответ: –1; 0; 4.Решение