Inegalitate conditionata cu produs
Posted: Fri May 01, 2009 9:42 pm
Fie \( a,b,c>0 \) astfel incat \( abc=1 \). Sa se arate ca :
\( \frac{1}{\sqrt{b+\frac{1}{a}+\frac{1}{2}}}+\frac{1}{\sqrt{c+\frac{1}{b}+\frac{1}{2}}}+\frac{1}{\sqrt{a+\frac{1}{c}+\frac{1}{2}}}\ge \sqrt{2} \)
\( \frac{1}{\sqrt{b+\frac{1}{a}+\frac{1}{2}}}+\frac{1}{\sqrt{c+\frac{1}{b}+\frac{1}{2}}}+\frac{1}{\sqrt{a+\frac{1}{c}+\frac{1}{2}}}\ge \sqrt{2} \)