Shortlist 9

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Antonache Emanuel
Euclid
Posts: 37
Joined: Sat Feb 28, 2009 4:15 pm
Location: Targoviste, Dambovita

Shortlist 9

Post by Antonache Emanuel »

Fie a,b,c numere strict pozitive, subunitare cu suma 1. Demonstrati ca:
\( \sum\frac{log^2_{ab}c}{a+b}\ge\frac{9}{8} \).
Tudorel Lupu, Constanta, Shortlist 2003
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Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

\( LHS\ge \frac{(\sum\log_{ab}c)^2}{2\sum a}\ge RHS \)
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