Задача 14. Решите уравнение \({\left( {2x-9} \right)^2}\left( {x-9} \right) = \left( {2x-9} \right){\left( {x-9} \right)^2}\)
ОТВЕТ: 0; 9/2; 9.
\({\left( {2x-9} \right)^2}\left( {x-9} \right) = \left( {2x-9} \right){\left( {x-9} \right)^2}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\left( {2x-9} \right)^2}\left( {x-9} \right)-\left( {2x-9} \right){\left( {x-9} \right)^2} = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\left( {2x-9} \right)\left( {x-9} \right)\left( {\left( {2x-9} \right)-\left( {x-9} \right)} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left( {2x-9} \right)\left( {x-9} \right)\left( {2x-9-x + 9} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,x\left( {2x-9} \right)\left( {x-9} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,\,\,\,\,}\\{2x-9 = 0,}\\{x-9 = 0\,\,}\end{array}} \right.\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,}\\{x = \dfrac{9}{2},}\\{x = 9.\,}\end{array}} \right.\) Ответ: \(0;\;\;\dfrac{9}{2};\;\;9.\)