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2012 Greece Team Selection Test
3
a+b+c=3
a+b+c=3
Source: Greek TST 2012,Pr.3
August 28, 2014
inequalities proposed
algebra
Inequality
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers satisfying
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
.Prove that
∑
s
y
m
a
2
(
b
+
c
)
3
≥
3
8
\sum_{sym} \frac{a^{2}}{(b+c)^{3}}\geq \frac{3}{8}
∑
sy
m
(
b
+
c
)
3
a
2
≥
8
3
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