Задача 9. Решите уравнение \(\sqrt {\frac{5}{{3 — 2x}}} = \frac{1}{9}.\)
Решение
\(\sqrt {\frac{5}{{3 — 2x}}} = \frac{1}{9}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\frac{5}{{3 — 2x}} = \frac{1}{{81}}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{3 — 2x \ne 0\,\,\,\,\,\,}\\{3 — 2x = 405}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x \ne 1,5\,\,\,}\\{x = — 201}\end{array}} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,x = — 201.\)
Ответ: – 201.