Shortlist 5

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

Shortlist 5

Post by Antonache Emanuel »

Se considera numerele complexe a,b,c distincte doua cate doua, astfel incat \( |a|=|b|=|c|=1 \) si \( |a-b|^2+|b-c|^2|c-a|^2>8 \). Sa se arate ca:
\( |(a+b)(b+c)(c+a)|<=1 \).
Dan Nedeianu, Drobeta Turnu Severin, Shortlist 2002
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