Задача 7. Решите уравнение \({\left( {x + 5} \right)^3} = 25\left( {x + 5} \right)\)
ОТВЕТ: -10; -5; 0.
\({\left( {x + 5} \right)^3} = 25\left( {x + 5} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\left( {x + 5} \right)^3}-25\left( {x + 5} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 5} \right)\left( {{{\left( {x + 5} \right)}^2}-{5^2}} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left( {x + 5} \right)\left( {x + 5-5} \right)\left( {x + 5 + 5} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \(\, \Leftrightarrow \,\,\,\,\,\,\,x\left( {x + 5} \right)\left( {x + 10} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,\,\,\,}\\{x + 5 = 0,\,\,}\\{x + 10 = 0}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 0,\,\,\,\,\,\,\,}\\{x = -5,\,\,}\\{x = -10.}\end{array}} \right.\) Ответ: –10; –5; 0