mateforum.ro

Determinati 3 numere reale strict pozitive \( x,\ y,\ z \) stiind ca \( \frac{1}{x^{2}+1}+\frac{1}{y^{2}+4}+\frac{1}{z^{2}+9}=\frac{7}{12}\sqrt{\frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{1}{z^{2}}} \).

Ovidiu Pop

Aplicand AM-GM si CBS obtinem egalitate si x=1, y=2, z=3.