Задача 6А. Решите уравнение \(\left| x \right| + 2 = 3\)
ОТВЕТ: -1; 1.Ответ
\(\left| x \right| + 2 = 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left| x \right| = 1.\) Уравнение вида \(\left| {f\left( x \right)} \right| = a\), где \(a \ge 0\), равносильно совокупности: \(\left[ {\begin{array}{*{20}{c}}{f\left( x \right) = a,\,\,\,}\\{f\left( x \right) = -a.}\end{array}} \right.\) \(\left| x \right| = 1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 1,\,\,\,\,}\\{x = -1.}\end{array}} \right.\) Ответ: \( \pm 1.\)Решение