Conditie non-standard (IMAR '05)
Posted: Mon Jun 16, 2008 7:46 pm
Fie \( a, b, c > 0 \) cu \( abc \ge 1 \). Aratati ca \( \sum \frac{1}{1 + b + c} \le 1 \).
\( abc=l\ge1 \) Notam \( A=\frac{a}{\sqrt[3]{l}} \) si analoagele. Avem ABC=1.
\( a\geq A\\\\b\ge B\\c\ge C \) si e suficient sa aratam ca \( \sum\frac{1}{1+A+B}\le1 \).