Inegalitate cu a, b, c, x, y, z

[Mateescu Constantin]

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

[Marius Mainea]

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