Задача 12А. Решите уравнение \(\left| {{x^2}-3x-2} \right| = 2\)
ОТВЕТ: -1; 0; 3; 4.
\(\left| {{x^2}-3x-2} \right| = 2.\) Уравнение вида \(\left| {f\left( x \right)} \right| = a\), где \(a \ge 0\), равносильно совокупности: \(\left[ {\begin{array}{*{20}{c}}{f\left( x \right) = a,\,\,\,}\\{f\left( x \right) = -a.}\end{array}} \right.\) \(\left| {{x^2}-3x-2} \right| = 2\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{{x^2}-3x-2 = 2,}\\{{x^2}-3x-2 = -2}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{{x^2}-3x-4 = 0,}\\{{x^2}-3x = 0\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = -1,}\\{x = 4,\,\,\,}\\{x = 0,\,\,\,}\\{x = 3.\,\,\,}\end{array}} \right.\) Ответ: \(-1;\;\;0;\;\;3;\;\;4.\)