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National and Regional Contests
India Contests
Regional Mathematical Olympiad
2016 India Regional Mathematical Olympiad
2
RMO 2016 ,Q2
RMO 2016 ,Q2
Source: Oct 23,2016
October 25, 2016
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers such that
a
b
1
+
b
c
+
b
c
1
+
c
a
+
c
a
1
+
a
b
=
1
\dfrac{ab}{1+bc}+\dfrac{bc}{1+ca}+\dfrac{ca}{1+ab}=1
1
+
b
c
ab
+
1
+
c
a
b
c
+
1
+
ab
c
a
=
1
. Prove that
1
a
3
+
1
b
3
+
1
c
3
≥
6
2
\dfrac{1}{a^3}+\dfrac{1}{b^3}+\dfrac{1}{c^3} \ge 6\sqrt{2}
a
3
1
+
b
3
1
+
c
3
1
≥
6
2
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