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Iran MO (3rd Round)
2017 Iran MO (3rd round)
3
Inequality
Inequality
Source: Iran 3rd round-2017-Algebra final exam-P3
September 2, 2017
algebra
Inequality
AM-GM
Iran
inequalities
Problem Statement
Let
a
,
b
a,b
a
,
b
and
c
c
c
be positive real numbers. Prove that
∑
c
y
c
a
3
b
(
3
a
+
2
b
)
3
≥
∑
c
y
c
a
2
b
c
(
2
a
+
2
b
+
c
)
3
\sum_{cyc} \frac {a^3b}{(3a+2b)^3} \ge \sum_{cyc} \frac {a^2bc}{(2a+2b+c)^3}
cyc
∑
(
3
a
+
2
b
)
3
a
3
b
≥
cyc
∑
(
2
a
+
2
b
+
c
)
3
a
2
b
c
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