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National and Regional Contests
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Indonesia MO
2003 Indonesia MO
5
A weak classic inequality
A weak classic inequality
Source: INAMO 2003 - Problem 5
August 5, 2011
inequalities
inequalities unsolved
Problem Statement
For any real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
, prove that
5
a
2
+
5
b
2
+
5
c
2
≥
4
a
b
+
4
a
c
+
4
b
c
5a^2 + 5b^2 + 5c^2 \ge 4ab + 4ac + 4bc
5
a
2
+
5
b
2
+
5
c
2
≥
4
ab
+
4
a
c
+
4
b
c
and determine when equality occurs.
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