Задача 8. Решите уравнение \(\sqrt {\frac{3}{{20 — 5x}}} = 0,2.\)
Решение
\(\sqrt {\frac{3}{{20 — 5x}}} = \frac{1}{5}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\frac{3}{{20 — 5x}} = \frac{1}{{25}}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{20 — 5x \ne 0\,\,}\\{20 — 5x = 75}\end{array}} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x \ne 4\,\,\,\,\,\,}\\{x = — 11}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x = — 11.\)
Ответ: – 11.