ОГЭ по математике. №20 Уравнения. ФИПИ. Задача 51

ОТВЕТ:  \(-4;\,\,\,\,-3;\,\,\,\,3.\)

\({x^3} + 4{x^2} = 9x + 36\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{x^3} + 4{x^2}-9x-36 = 0.\)

Разложим левую часть полученного уравнения на множители методом группировки:

\({x^3} + 4{x^2}-9x-36 = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{x^2}\left( {x + 4} \right)-9\left( {x + 4} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left( {x + 4} \right)\left( {{x^2}-9} \right) = 0\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x + 4 = 0,\\{x^2}-9 = 0\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x = -4,\\\left( {x-3} \right)\left( {x + 3} \right) = 0\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x = -4,\\x-3 = 0,\\x + 3 = 0\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left[ \begin{array}{l}x = -4,\\x = 3,\\x = -3.\end{array} \right.\)

Ответ:  \(-4;\,\,\,\,-3;\,\,\,\,3.\)