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2015 Azerbaijan JBMO TST
2015 Azerbaijan JBMO TST
Source: 2015 Azerbaijan JBMO TST
May 2, 2015
algebra
inequalities
Azerbaijan
Problem Statement
With the conditions
a
,
b
,
c
∈
R
+
a,b,c\in\mathbb{R^+}
a
,
b
,
c
∈
R
+
and
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
, prove that
7
+
2
b
1
+
a
+
7
+
2
c
1
+
b
+
7
+
2
a
1
+
c
≥
69
4
\frac{7+2b}{1+a}+\frac{7+2c}{1+b}+\frac{7+2a}{1+c}\geq\frac{69}{4}
1
+
a
7
+
2
b
+
1
+
b
7
+
2
c
+
1
+
c
7
+
2
a
≥
4
69
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