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2017 JBMO Shortlist
A3
Inequality
Inequality
Source:
March 31, 2018
inequalities
JBMO Shortlist
Problem Statement
let
a
≤
b
≤
c
≤
d
a\le b\le c \le d
a
≤
b
≤
c
≤
d
show that:
a
b
3
+
b
c
3
+
c
d
3
+
d
a
3
≥
a
2
b
2
+
b
2
c
2
+
c
2
d
2
+
d
2
a
2
ab^3+bc^3+cd^3+da^3\ge a^2b^2+b^2c^2+c^2d^2+d^2a^2
a
b
3
+
b
c
3
+
c
d
3
+
d
a
3
≥
a
2
b
2
+
b
2
c
2
+
c
2
d
2
+
d
2
a
2
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