Shortlist 5
Posted: Sun Mar 28, 2010 7:30 pm
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
\( |(a+b)(b+c)(c+a)|<=1 \).
Dan Nedeianu, Drobeta Turnu Severin, Shortlist 2002