MathDB
Problems
Contests
National and Regional Contests
Thailand Contests
Thailand TST Selection Test
2022 Thailand TSTST
2
Cringe IE
Cringe IE
Source: 2021 Thailand October Camp 1.2
May 6, 2023
inequalities
Problem Statement
Let
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
satisfy
a
≥
b
≥
c
a\geq b\geq c
a
≥
b
≥
c
. Prove that
4
a
2
(
b
+
c
)
+
4
b
2
(
c
+
a
)
+
4
c
2
(
a
+
b
)
≤
(
∑
c
y
c
a
2
+
1
b
2
)
(
∑
c
y
c
b
3
a
2
(
a
3
+
2
b
3
)
)
.
\frac{4}{a^2(b+c)}+\frac{4}{b^2(c+a)}+\frac{4}{c^2(a+b)} \leq \left(\sum_{cyc} \frac{a^2+1} {b^2} \right)\left(\sum_{cyc} \frac{b^3}{a^2(a^3+2b^3)}\right).
a
2
(
b
+
c
)
4
+
b
2
(
c
+
a
)
4
+
c
2
(
a
+
b
)
4
≤
(
cyc
∑
b
2
a
2
+
1
)
(
cyc
∑
a
2
(
a
3
+
2
b
3
)
b
3
)
.
Back to Problems
View on AoPS