Inegalitate exponentiala si liniara

[Andrei Velicu]

Fie \( m,n,p \in \mathbb{N} \) si \( x, y, x \in \mathbb{R} \) astfel incat \( 2^mx+2^ny+2^pz\geq 0 \). Sa se arate ca:
\( 2^m(2^x-1)+2^n(2^y-1)+2^p(2^z-1) \geq 0 \).

Cristinel Mortici, "Nicolae Coculescu" 2007