IMAC 2010 Ziua a doua Problema 6
Posted: Wed Jun 16, 2010 4:02 pm
Fie numerele reale \( a,b,c\in[0,\infty) \) astfel incat \( a+b+c=2 \). Sa se arate ca:
\( \frac{bc}{\sqrt[4]{3a^2+4}}+\frac{ca}{\sqrt[4]{3b^2+4}}+\frac{ab}{\sqrt[4]{3c^2+4}}\le\frac{2*\sqrt[4]{3}}{3} \)
Spania
\( \frac{bc}{\sqrt[4]{3a^2+4}}+\frac{ca}{\sqrt[4]{3b^2+4}}+\frac{ab}{\sqrt[4]{3c^2+4}}\le\frac{2*\sqrt[4]{3}}{3} \)
Spania