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Mediterranean Mathematics Olympiad
2003 Mediterranean Mathematics Olympiad
3
3
Part of
2003 Mediterranean Mathematics Olympiad
Problems
(1)
Maybe old inequality with a+b+c=3
Source: Mediterranean MO 2003
10/31/2010
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be non-negative numbers with
a
+
b
+
c
=
3
a+b+c = 3
a
+
b
+
c
=
3
. Prove the inequality
a
b
2
+
1
+
b
c
2
+
1
+
c
a
2
+
1
≥
3
2
.
\frac{a}{b^2+1}+\frac{b}{c^2+1}+\frac{c}{a^2+1} \geq \frac 32.
b
2
+
1
a
+
c
2
+
1
b
+
a
2
+
1
c
≥
2
3
.
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