Cho a + 5/a - 5 = b + 6/b - 6. (a khác 5, b khác 6). Chứng minh a/b = 5/6
Cho \(a + \frac{5}{a} - 5 = b + \frac{6}{b} - 6\). (a khác 5, b khác 6). Chứng minh \(\frac{a}{b} = \frac{5}{6}\)
Lời giải
\(\frac{{a + 5}}{{a - 5}} = \frac{{b + 6}}{{b - 6}}\)
\(\frac{{a - 5}}{{a - 5}} + \frac{{10}}{{a - 5}} = \frac{{b - 6}}{{b - 6}} + \frac{{12}}{{b - 6}}\)
\(1 + \frac{{10}}{{a - 5}} = 1 + \frac{{12}}{{b - 6}}\)
\(\frac{{10}}{{a - 5}} = \frac{{12}}{{b - 6}}\)
\( \Rightarrow 12(a - 5) = 10(b - 6)\)
\( \Rightarrow 6(a - 5) = 5(b - 6)\)
\( \Rightarrow \) 6a – 30 = 5b – 30
\( \Rightarrow \) 6a = 5b
\( \Rightarrow \) \(\frac{a}{b} = \frac{5}{6}\)