Задача 9. Решите уравнение \({\left( {x-2} \right)^2}\left( {x-3} \right) = 12\left( {x-2} \right)\)
ОТВЕТ: -1; 2; 6.
\({\left( {x-2} \right)^2}\left( {x-3} \right) = 12\left( {x-2} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\left( {x-2} \right)^2}\left( {x-3} \right)-12\left( {x-2} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,\left( {x-2} \right)\left( {\left( {x-2} \right)\left( {x-3} \right)-12} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left( {x-2} \right)\left( {{x^2}-5x-6} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x-2 = 0,\,\,\,\,\,\,\,\,\,\,\,\,}\\{{x^2}-5x-6 = 0}\end{array}} \right.\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 2,\,\,\,}\\{x = -1,}\\{x = 6.\,\,}\end{array}} \right.\) Ответ: –1; 2; 6.