Inegalitate hard

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alex2008
Leibniz
Posts: 464
Joined: Sun Oct 19, 2008 3:23 pm
Location: Tulcea

Inegalitate hard

Post by alex2008 »

Fie \( x,y,z>0 \) astfel incat \( x^2y+y^2z+z^2x=9 \). Sa se demonstreze ca:

\( \frac{xy}{z(x^2+yz)^2}+\frac{yz}{x(y^2+zx)^2}+\frac{zx}{y(z^2+xy)^2}\ge \frac{1}{4}. \)
. A snake that slithers on the ground can only dream of flying through the air.
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