Inegalitate conditionata cu suma variabilelor
Posted: Mon Apr 14, 2008 11:50 pm
Fie \( a,b,c>0 \) a.i. \( a+b+c=3 \). Aratati ca
\( \frac{1}{2+a^2b}+\frac{1}{2+b^2c}+\frac{1}{2+c^2a}\leq \frac{a^3+b^3+c^3}{2+abc} \).
\( \frac{1}{2+a^2b}+\frac{1}{2+b^2c}+\frac{1}{2+c^2a}\leq \frac{a^3+b^3+c^3}{2+abc} \).