Inegalitate cu trei variabile in [1,2]
Posted: Thu Apr 30, 2009 10:18 pm
Fie \( a,b,c\in [1,2] \) . Sa se demonstreze ca :
\(
\frac{b\sqrt{a}}{4b\sqrt{c}-c\sqrt{a}}+\frac{c\sqrt{b}}{4c\sqrt{a}-a\sqrt{b}}+\frac{a\sqrt{c}}{4a\sqrt{b}-b\sqrt{c}}\ge 1 \)
\(
\frac{b\sqrt{a}}{4b\sqrt{c}-c\sqrt{a}}+\frac{c\sqrt{b}}{4c\sqrt{a}-a\sqrt{b}}+\frac{a\sqrt{c}}{4a\sqrt{b}-b\sqrt{c}}\ge 1 \)