Tìm x biết: \(\frac{{x + 2011}}{{2013}} + \frac{{x + 2012}}{{2012}} = \frac{{x + 2010}}{{2014}} + \frac{{x + 2013}}{{2011}}\).
Trả lời
\(\frac{{x + 2011}}{{2013}} + \frac{{x + 2012}}{{2012}} = \frac{{x + 2010}}{{2014}} + \frac{{x + 2013}}{{2011}}\)
⇔ \(\frac{{x + 2011}}{{2013}} + 1 + \frac{{x + 2012}}{{2012}} + 1 = \frac{{x + 2010}}{{2014}} + 1 + \frac{{x + 2013}}{{2011}} + 1\)
⇔ \(\frac{{x + 4024}}{{2013}} + \frac{{x + 4024}}{{2012}} = \frac{{x + 4024}}{{2014}} + \frac{{x + 4024}}{{2011}}\)
⇔ \(\left( {x + 4024} \right)\left( {\frac{1}{{2013}} + \frac{1}{{2012}} - \frac{1}{{2014}} - \frac{1}{{2011}}} \right) = 0\)
Vì \(\frac{1}{{2013}} + \frac{1}{{2012}} - \frac{1}{{2014}} - \frac{1}{{2011}} \ne 0\) nên x + 4024 = 0
Hay x = –4024.
Vậy x = –4024.
