ОГЭ по математике. №20 Уравнения. ФИПИ. Задача 43

ОТВЕТ:  \(-4;\,\,\,\,-1;\,\,\,\,1.\)

Разложим левую часть исходного уравнения на множители методом группировки:

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

\( \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x + 4 = 0,\\{x^2}-1 = 0\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x = -4,\\\left( {x + 1} \right)\left( {x-1} \right) = 0\end{array} \right.\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ \begin{array}{l}x = -4,\\x + 1 = 0,\\x-1 = 0\end{array} \right.\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left[ \begin{array}{l}x = -4,\\x = -1,\\x = 1.\end{array} \right.\)

Ответ:  \(-4;\,\,\,\,-1;\,\,\,\,1.\)