Задача 16. Решите уравнение    \({x^3}-3{x^2} = 4x\)

Ответ

ОТВЕТ: -1;  0;  4.

Решение

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

\( \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\\{{x^2}-3x-4 = 0}\end{array}} \right.\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,}\\{x = -1,}\\{x = 4.\,\,}\end{array}} \right.\)

Ответ:  –1;  0;  4.