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Contest of the Centers of Excellency of Suceava
2019 Centers of Excellency of Suceava
1
Four term - inequality
Four term - inequality
Source: 2019 contest
July 6, 2020
inequalitites
inequalities
Problem Statement
For
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
positive, prove:
2
a
a
2
+
b
c
+
2
b
b
2
+
c
d
+
2
c
c
2
+
d
a
+
2
d
d
2
+
a
b
≤
1
a
+
1
b
+
1
c
+
1
d
\frac{2a}{a^2+bc} +\frac{2b}{b^2+cd} +\frac{2c}{c^2+da} +\frac{2d}{d^2+ab}\le \frac{1}{a} +\frac{1}{b} +\frac{1}{c} +\frac{1}{d}
a
2
+
b
c
2
a
+
b
2
+
c
d
2
b
+
c
2
+
d
a
2
c
+
d
2
+
ab
2
d
≤
a
1
+
b
1
+
c
1
+
d
1
Dan Popescu
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