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National and Regional Contests
Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 2
2019 Nigeria Senior MO Round 2
5
Murihead inequality
Murihead inequality
Source: Nigerian senior mathematics Olympiad round 2 no 5
September 8, 2019
inequalities
Problem Statement
Let
a
a
a
,
b
b
b
, and
c
c
c
be real numbers such that
a
b
c
=
1
abc=1
ab
c
=
1
. prove that
1
+
a
+
a
b
1
+
b
+
a
b
\frac{1+a+ab}{1+b+ab}
1
+
b
+
ab
1
+
a
+
ab
+
1
+
b
+
b
c
1
+
c
+
b
c
\frac{1+b+bc}{1+c+bc}
1
+
c
+
b
c
1
+
b
+
b
c
+
1
+
c
+
a
c
1
+
a
+
a
c
\frac{1+c+ac}{1+a+ac}
1
+
a
+
a
c
1
+
c
+
a
c
>
=
3
>=3
>=
3
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