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Mexico Contests
Regional Olympiad of Mexico Center Zone
2010 Regional Olympiad of Mexico Center Zone
3
inequality
inequality
Source: Mexico Regional Math Olympiad 2010 Problem 3
September 6, 2015
inequalities
Problem Statement
Let
a
a
a
,
b
b
b
and
c
c
c
be real positive numbers such that
1
a
+
1
b
+
1
c
=
1
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1
a
1
+
b
1
+
c
1
=
1
Prove that:
a
2
+
b
2
+
b
2
≥
2
a
+
2
b
+
2
c
+
9
a^2+b^2+b^2 \ge 2a+2b+2c+9
a
2
+
b
2
+
b
2
≥
2
a
+
2
b
+
2
c
+
9
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