Inegalitate conditionata

Moderators: Laurian Filip, Beniamin Bogosel, Filip Chindea

Post Reply
Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Inegalitate conditionata

Post by Marius Mainea »

Fie a,b,c \( \geq 0 \) cu proprietatea ca a+b+c=1. Sa se arate ca :

\( \frac{1}{3}\leq \frac{a}{a^2+a+1}+\frac{b}{b^2+b+1}+\frac{c}{c^2+c+1}\leq \frac{9}{13} \)

Ion Nedelcu SHL 2008
Top
opincariumihai
Thales
Posts: 134
Joined: Sat May 09, 2009 7:45 pm
Location: BRAD

Se poate folosi convexitatea

Post by opincariumihai »

Functia \( f:[0.1]\to R \), \( f(x)=\frac{x}{1+x+x^2} \) este concava.
Cum justificam la nivelul clasei a IX-a ?
Top
Post Reply

Return to “Clasa a IX-a”