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Inegalitate atipica 2
Posted: Fri Aug 01, 2008 10:20 pm
by Marius Mainea
Daca \( a,b,c\in[-1,2] \) si \( a+b+c=0 \) atunci \( a^2+b^2+c^2\le 6 \).
Posted: Sat Aug 02, 2008 4:00 pm
by Sorin
Avem ca \( (a+1)(a-2) \) \( \leq 0 \) \( (1) \) \( \Leftrightarrow \) \( a^2 - a - 2 \) \( \leq 0 \) \( \Leftrightarrow \) \( a^2 \) \( \leq \) \( a+2 \) . Aplicand analog \( (1) \) pt b si c si din \( a+b+c=0 \) obtinem qed.