Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 972

\[\frac{1}{a},\ \frac{1}{b}\ и\ \frac{1}{c} - данные\ дроби.\]

\[1)\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1\]

\[\frac{1}{a} + \frac{1}{b} = 1 - \frac{1}{c}.\]

\[2)\ \frac{1}{a} + \frac{1}{b} = 5\left( \frac{1}{c} \right)\]

\[1 - \frac{1}{c} = \frac{5}{c}\]

\[\frac{6}{c} = 1\]

\[c = 6.\]

\[\frac{1}{a} + \frac{1}{b} = \frac{5}{6}\]

\[\frac{1}{a} = \frac{5}{6} - \frac{1}{b}.\]

\[3)\ \frac{1}{a} - \frac{1}{b} = \frac{1}{c}\]

\[\frac{5}{6} - \frac{1}{b} - \frac{1}{b} = \frac{1}{6}\]

\[\frac{2}{b} = \frac{4}{6}\]

\[4b = 12\]

\[b = 3.\]

\[\frac{1}{a} = \frac{5}{6} - \frac{1}{3} = \frac{1}{2}\]

\[a = 2.\]

\[Ответ:\ \ \frac{1}{2};\ \frac{1}{3};\ \frac{1}{6}.\]