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Posted: **Sun Feb 01, 2009 1:05 pm**

Sa se rezolve in \( \mathbb{R} \) ecuatia:

\( \sum_{cyc}\sqrt{\frac{x}{y+z}}=\frac{3}{2} \).

Eleodor Popescu, Etapa locala Mehedinti 2006

Posted: **Sun Feb 01, 2009 2:05 pm**

\( \frac{3}{2}=\sum{\sqrt{\frac{x}{y+z}}}\ge \sum{\frac{2}{\frac{y+z}{x}+1}}=\sum{\frac{2x}{x+y+z}}=2 \)

Rezulta ca ecuatia nu are solutii.