MathDB
Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2004 Switzerland Team Selection Test
4
Swiss IMO TST 2004
Swiss IMO TST 2004
Source: abc=1
October 8, 2006
inequalities
inequalities unsolved
Problem Statement
Second Test, May 16 Let
a
a
a
,
b
b
b
, and
c
c
c
be positive real numbers such that
a
b
c
=
1
abc = 1
ab
c
=
1
. Prove that
a
b
a
5
+
b
5
+
a
b
+
b
c
b
5
+
c
5
+
b
c
+
c
a
c
5
+
a
5
+
c
a
≤
1
\frac{ab}{a^{5}+b^{5}+ab}+\frac{bc}{b^{5}+c^{5}+bc}+\frac{ca}{c^{5}+a^{5}+ca}\le 1
a
5
+
b
5
+
ab
ab
+
b
5
+
c
5
+
b
c
b
c
+
c
5
+
a
5
+
c
a
c
a
≤
1
. When does equality hold?
Back to Problems
View on AoPS