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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2018 Moldova Team Selection Test
6
folklore
folklore
Source: Moldova TST 2018, b6
April 6, 2018
inequalities
three variable inequality
algebra
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers such that
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
. Show that
a
1
+
b
2
+
b
1
+
c
2
+
c
1
+
a
2
≥
3
2
.
\frac{a}{1+b^2}+\frac{b}{1+c^2}+\frac{c}{1+a^2}\geq \frac{3}{2}.
1
+
b
2
a
+
1
+
c
2
b
+
1
+
a
2
c
≥
2
3
.
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