Задача 4. Найдите \(\frac{a}{b}\), если \(\frac{{2a + 5b}}{{5a + 2b}} = 1\).
Решение
\(\frac{{2a + 5b}}{{5a + 2b}} = 1\,\,\,\,\, \Leftrightarrow \,\,\,\,\,2a + 5b = 5a + 2b\,\,\,\,\, \Leftrightarrow \,\,\,\,\,3b = 3a\,\left| {\,:\,} \right.3\,\,\,\,\, \Leftrightarrow \,\,\,\,\,a = b\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\frac{a}{b} = 1.\)
Ответ: 1.