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Jozsef Wildt International Math Competition
2019 Jozsef Wildt International Math Competition
W. 61
Prove this 3 real number variable inequality
Prove this 3 real number variable inequality
Source: 2019 Jozsef Wildt International Math Competition
May 20, 2020
Summation
inequalities
Problem Statement
If
a
a
a
,
b
b
b
,
c
∈
R
c \in \mathbb{R}
c
∈
R
then
∑
c
y
c
(
c
+
a
)
2
b
2
+
c
2
a
2
+
5
∣
∑
c
y
c
a
b
∣
≥
∑
c
y
c
(
a
b
+
2
b
c
+
c
a
)
2
+
(
b
+
c
)
2
a
2
\sum \limits_{cyc} \sqrt{(c+a)^2b^2+c^2a^2}+\sqrt{5}\left |\sum \limits_{cyc} \sqrt{ab}\right |\geq \sum \limits_{cyc}\sqrt{(ab+2bc+ca)^2+(b+c)^2a^2}
cyc
∑
(
c
+
a
)
2
b
2
+
c
2
a
2
+
5
cyc
∑
ab
≥
cyc
∑
(
ab
+
2
b
c
+
c
a
)
2
+
(
b
+
c
)
2
a
2
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