MathDB
Problems
Contests
International Contests
Czech-Polish-Slovak Match
2000 Czech and Slovak Match
1
1
Part of
2000 Czech and Slovak Match
Problems
(1)
a,b,c are sidelengths if 5abc>a^3+b^3+c^3
Source: Czech and Slovak Match 2000 P1
12/5/2022
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive real numbers which satisfy
5
a
b
c
>
a
3
+
b
3
+
c
3
5abc>a^3+b^3+c^3
5
ab
c
>
a
3
+
b
3
+
c
3
. Prove that
a
,
b
,
c
a,b,c
a
,
b
,
c
can form a triangle.
geometry
Geometric Inequalities
inequalities
algebra