Inegalitate hard
Posted: Sun May 24, 2009 7:36 pm
Fie \( x,y,z>0 \) astfel incat \( x^2y+y^2z+z^2x=9 \). Sa se demonstreze ca:
\( \frac{xy}{z(x^2+yz)^2}+\frac{yz}{x(y^2+zx)^2}+\frac{zx}{y(z^2+xy)^2}\ge \frac{1}{4}. \)
\( \frac{xy}{z(x^2+yz)^2}+\frac{yz}{x(y^2+zx)^2}+\frac{zx}{y(z^2+xy)^2}\ge \frac{1}{4}. \)