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International Contests
IMO Shortlist
1996 IMO Shortlist
1
Inequality 15
Inequality 15
Source: IMO 1996 Shortlist
September 13, 2003
inequalities
three variable inequality
algebra
IMO Shortlist
Problem Statement
Suppose that
a
,
b
,
c
>
0
a, b, c > 0
a
,
b
,
c
>
0
such that
a
b
c
=
1
abc = 1
ab
c
=
1
. Prove that
a
b
a
b
+
a
5
+
b
5
+
b
c
b
c
+
b
5
+
c
5
+
c
a
c
a
+
c
5
+
a
5
≤
1.
\frac{ab}{ab + a^5 + b^5} + \frac{bc}{bc + b^5 + c^5} + \frac{ca}{ca + c^5 + a^5} \leq 1.
ab
+
a
5
+
b
5
ab
+
b
c
+
b
5
+
c
5
b
c
+
c
a
+
c
5
+
a
5
c
a
≤
1.
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