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National and Regional Contests
Thailand Contests
Thailand TST Selection Test
2017 Thailand TSTST
3
Weird Inequality
Weird Inequality
Source: 2016 Thailand October Camp 3.3
February 28, 2022
inequalities
Problem Statement
Let
a
,
b
,
c
∈
R
+
a, b, c \in\mathbb{R}^+
a
,
b
,
c
∈
R
+
. Prove that
∑
c
y
c
a
b
(
1
2
a
+
c
+
1
2
b
+
c
)
<
∑
c
y
c
a
3
+
b
3
c
2
+
a
b
.
\sum_{cyc}ab\left(\frac{1}{2a+c}+\frac{1}{2b+c}\right)<\sum_{cyc}\frac{a^3+b^3}{c^2+ab}.
cyc
∑
ab
(
2
a
+
c
1
+
2
b
+
c
1
)
<
cyc
∑
c
2
+
ab
a
3
+
b
3
.
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