Задача 19. Решите уравнение \(2{x^3}-5{x^2}-2x + 5 = 0\)
ОТВЕТ: -1; 1; 2,5.Ответ
\(2{x^3}-5{x^2}-2x + 5 = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^2}\left( {2x-5} \right)-\left( {2x-5} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \) \( \Leftrightarrow \,\,\,\,\,\,\,\left( {2x-5} \right)\left( {{x^2}-1} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{2x-5 = 0,}\\{{x^2}-1 = 0\,\,}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \frac{5}{2},}\\{x = -1,}\\{x = 1.\,\,}\end{array}} \right.\) Ответ: –1; 1; 2,5.Решение