IMO Shortlist 2010 problem A8


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 9,0
Dodao/la: arhiva
23. lipnja 2013.
LaTeX PDF
Given six positive numbers a,b,c,d,e,f such that a < b < c < d < e < f. Let a+c+e=S and b+d+f=T. Prove that
2ST > \sqrt{3(S+T)\left(S(bd + bf + df) + T(ac + ae + ce) \right)}.


Proposed by Sung Yun Kim, South Korea
Izvor: Međunarodna matematička olimpijada, shortlist 2010