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National and Regional Contests
India Contests
India IMO Training Camp
2002 India IMO Training Camp
5
easy inequality with a^2+b^2+c^2=3abc
easy inequality with a^2+b^2+c^2=3abc
Source:
June 29, 2012
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive reals such that
a
2
+
b
2
+
c
2
=
3
a
b
c
a^2+b^2+c^2=3abc
a
2
+
b
2
+
c
2
=
3
ab
c
. Prove that
a
b
2
c
2
+
b
c
2
a
2
+
c
a
2
b
2
≥
9
a
+
b
+
c
\frac{a}{b^2c^2}+\frac{b}{c^2a^2}+\frac{c}{a^2b^2} \geq \frac{9}{a+b+c}
b
2
c
2
a
+
c
2
a
2
b
+
a
2
b
2
c
≥
a
+
b
+
c
9
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