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Spain Mathematical Olympiad
2010 Spain Mathematical Olympiad
1
Spain MO 4 - Inequality
Spain MO 4 - Inequality
Source: Spain MO 2010
August 16, 2010
inequalities
three variable inequality
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be three positive real numbers. Show that
a
+
b
+
3
c
3
a
+
3
b
+
2
c
+
a
+
3
b
+
c
3
a
+
2
b
+
3
c
+
3
a
+
b
+
c
2
a
+
3
b
+
3
c
≥
15
8
\frac {a+b+3c}{3a+3b+2c}+\frac {a+3b+c}{3a+2b+3c}+\frac {3a+b+c}{2a+3b+3c} \ge \frac {15}{8}
3
a
+
3
b
+
2
c
a
+
b
+
3
c
+
3
a
+
2
b
+
3
c
a
+
3
b
+
c
+
2
a
+
3
b
+
3
c
3
a
+
b
+
c
≥
8
15
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