« Vrati se
Show that if a, b, c are the lengths of the sides of a triangle and if 2S = a + b + c, then
\frac{a^n}{b+c} + \frac{b^n}{c+a} +\frac{c^n}{a+b} \geq \left(\dfrac 23 \right)^{n-2}S^{n-1} \quad \forall n \in \mathbb N

Proposed by Greece.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1972IMO Shortlist 1997 problem 160
1744IMO Shortlist 1989 problem 60
1734IMO Shortlist 1988 problem 270
1314IMO Shortlist 1968 problem 90
1250IMO Shortlist 1967 problem 40
1149IMO Shortlist 1960 problem 31