Задача 11. Решите уравнение \(\left( {x-1} \right)\left( {{x^2} + 4x + 4} \right) = 4\left( {x + 2} \right)\)
ОТВЕТ: -3; -2; 2.
\(\left( {x-1} \right)\left( {{x^2} + 4x + 4} \right) = 4\left( {x + 2} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left( {x-1} \right){\left( {x + 2} \right)^2}-4\left( {x + 2} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 2} \right)\left( {\left( {x-1} \right)\left( {x + 2} \right)-4} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 2} \right)\left( {{x^2} + x-6} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x + 2 = 0,\,\,\,\,\,\,\,\,\,}\\{{x^2} + x-6 = 0}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = -2,}\\{x = -3,}\\{x = 2.\,\,}\end{array}} \right.\) Ответ: –3; –2; 2.