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

Shortlist 11

Post by Antonache Emanuel »

Fie a,b,c numere strict pozitive satisfacand \( a^3+b^3+c^3=1 \). Aratati ca:
\( \sum log_a (\sqrt[3]3bc)>0 \).
I. V. Maftei, Bucuresti
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Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

Notam \( x=a^3 \) si analoagele si inegalitatea se reduce la

\( \sum \log_x3yz>0 \) cu x,y,z pozitive cu \( x+y+z=1 \)
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