ОГЭ по математике. №20 Уравнения. ФИПИ. Задача 55

ОТВЕТ:  \(-5;\,\,\,\,-2;\,\,\,\,2.\)

\({x^3} + 5{x^2} = 4x + 20\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{x^3} + 5{x^2}-4x-20 = 0.\)

Разложим левую часть полученного уравнения на множители методом группировки:

\({x^3} + 5{x^2}-4x-20 = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{x^2}\left( {x + 5} \right)-4\left( {x + 5} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left( {x + 5} \right)\left( {{x^2}-4} \right) = 0\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x + 5 = 0,\\{x^2}-4 = 0\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x = -5,\\\left( {x-2} \right)\left( {x + 2} \right) = 0\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x = -5,\\x-2 = 0,\\x + 2 = 0\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x = -5,\\x = 2,\\x = -2.\end{array} \right.\)

Ответ:  \(-5;\,\,\,\,-2;\,\,\,\,2.\)