Inegalitate cu a, b, c, x, y, z
Posted: Sat Jun 20, 2009 12:26 pm
Fie \( a,\ b,\ c,\ x,\ y,\ z\in\mathbb{R} \) astfel incat \( a+b+c=x^2+y^2+z^2=1 \). Aratati ca: \( a(x+b)+b(y+c)+c(z+a)<1 \).
Concursul Nicolae Paun, 2002
Concursul Nicolae Paun, 2002