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National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2002 Iran MO (3rd Round)
16
Iran 2002
Iran 2002
Source: Iran selection test 2002
April 3, 2004
quadratics
Iran
Inequality
algebra
Problem Statement
For positive
a
,
b
,
c
a,b,c
a
,
b
,
c
,
a
2
+
b
2
+
c
2
+
a
b
c
=
4
a^{2}+b^{2}+c^{2}+abc=4
a
2
+
b
2
+
c
2
+
ab
c
=
4
Prove
a
+
b
+
c
≤
3
a+b+c \leq3
a
+
b
+
c
≤
3
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