Профиль №13. Рациональные уравнения. Задача 19А

ОТВЕТ: -1;  1;  2,5.

\(2{x^3}-5{x^2}-2x + 5 = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{x^2}\left( {2x-5} \right)-\left( {2x-5} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\,\,\left( {2x-5} \right)\left( {{x^2}-1} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{2x-5 = 0,}\\{{x^2}-1 = 0\,\,}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \dfrac{5}{2},}\\{x = -1,}\\{x = 1.\,\,}\end{array}} \right.\)

Ответ:  –1;  1;  2,5.