Рациональные уравнения. Задача 15

Рациональные уравнения. Задача 15math100admin44242024-05-27T20:46:53+03:00

Задача 15. Решите уравнение \({x^3} = 4{x^2} + 5x\)

Ответ

ОТВЕТ: -1; 0; 5.

Решение

\({x^3} = 4{x^2} + 5x\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^3}-4{x^2}-5x = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\left( {{x^2}-4x-5} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\\{{x^2}-4x-5 = 0}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,}\\{x = -1,}\\{x = 5.\,\,}\end{array}} \right.\)

Ответ: –1; 0; 5.