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National and Regional Contests
Azerbaijan Contests
JBMO TST - Azerbaijan
2016 Azerbaijan JBMO TST
1
inequalities
inequalities
Source:
April 24, 2023
Inequalites
inequalities
Problem Statement
Let
a
,
b
,
c
≥
0
a,b,c \ge 0
a
,
b
,
c
≥
0
and
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
. Prove that:
2
(
a
b
+
b
c
+
c
a
)
−
3
a
b
c
≥
∑
c
y
c
a
b
2
+
c
2
2
2(ab+bc+ca)-3abc\ge \sum_{cyc}^{}a\sqrt{\frac{b^2+c^2}{2}}
2
(
ab
+
b
c
+
c
a
)
−
3
ab
c
≥
∑
cyc
a
2
b
2
+
c
2
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