Concursul "Nicolae Paun", 2008, problema 1
Posted: Sat Dec 13, 2008 8:05 pm
Fie \( a,b,c \) numere reale strict pozitive astfel incat \( a^2+b^2+c^2=1 \). Demonstrati ca:
\( \frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\geq 3+\frac{2(a^3+b^3+c^3)}{abc} \).
\( \frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\geq 3+\frac{2(a^3+b^3+c^3)}{abc} \).