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Serbia JBMO TST
2011 Serbia JBMO TST
4
minimum
minimum
Source:
November 24, 2013
inequalities
Problem Statement
If a, b, c are positive real numbers with
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
. Find the minimum value of
a
+
b
+
c
+
1
a
b
c
\sqrt{a}+\sqrt{b}+\sqrt{c}+\frac{1}{\sqrt{abc}}
a
+
b
+
c
+
ab
c
1
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