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National and Regional Contests
Moldova Contests
EGMO TST - Moldova
2017 Moldova EGMO TST
1
Cyclic Inequality
Cyclic Inequality
Source: Moldova egmo tst problem1
November 7, 2016
inequalities
Problem Statement
Let
a
,
b
,
c
≥
0
a,b,c\geq 0
a
,
b
,
c
≥
0
. Prove:
1
+
a
+
a
2
1
+
b
+
c
2
+
1
+
b
+
b
2
1
+
c
+
a
2
+
1
+
c
+
c
2
1
+
a
+
b
2
≥
3
\frac{1+a+a^{2}}{1+b+c^{2}}+\frac{1+b+b^{2}}{1+c+a^{2}}+\frac{1+c+c^{2}}{1+a+b^{2}}\geq 3
1
+
b
+
c
2
1
+
a
+
a
2
+
1
+
c
+
a
2
1
+
b
+
b
2
+
1
+
a
+
b
2
1
+
c
+
c
2
≥
3
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