« Vrati se
Let a, b, c be positive real numbers such that \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = a+b+c. Prove that:
\frac{1}{(2a+b+c)^2}+\frac{1}{(a+2b+c)^2}+\frac{1}{(a+b+2c)^2}\leq \frac{3}{16}


Proposed by Juhan Aru, Estonia

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1983IMO Shortlist 1998 problem A112
2066IMO Shortlist 2001 problem A29
2206IMO Shortlist 2006 problem A31
2207IMO Shortlist 2006 problem A43
2266IMO Shortlist 2008 problem A36
2351Mala olimpijada 1998 zadatak 32