Inegalitate
Posted: Fri Feb 06, 2009 2:09 pm
Daca \( a,b,c,x,y,z,t \) sunt numere reale pozitive, demonstrati inegalitatea:
\( \frac{1}{ax+by+cz}+\frac{1}{ay+bz+ct}+\frac{1}{az+bt+cx}+\frac{1}{at+bx+cy}>\frac{8\sqrt{3}}{\sqrt{a^2+b^2+c^2}\cdot\sqrt{x^2+y^2+z^2+t^2}}. \)
D.M. Batinetu-Giurgiu
\( \frac{1}{ax+by+cz}+\frac{1}{ay+bz+ct}+\frac{1}{az+bt+cx}+\frac{1}{at+bx+cy}>\frac{8\sqrt{3}}{\sqrt{a^2+b^2+c^2}\cdot\sqrt{x^2+y^2+z^2+t^2}}. \)
D.M. Batinetu-Giurgiu