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Serbia Contests
Serbia JBMO TST
2016 Junior Balkan Team Selection Test
4
Serbia Junior TST 2016
Serbia Junior TST 2016
Source: Serbia Junior TST 2016 P4
May 21, 2016
Inequality
inequalities
Problem Statement
Let
a
,
b
,
c
∈
R
+
a,b,c\in \mathbb{R}^+
a
,
b
,
c
∈
R
+
, prove that:
2
a
3
a
+
b
+
2
b
3
b
+
c
+
2
c
3
c
+
a
≤
3
(
a
+
b
+
c
)
\frac{2a}{\sqrt{3a+b}}+\frac{2b}{\sqrt{3b+c}}+\frac{2c}{\sqrt{3c+a}}\leq \sqrt{3(a+b+c)}
3
a
+
b
2
a
+
3
b
+
c
2
b
+
3
c
+
a
2
c
≤
3
(
a
+
b
+
c
)
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