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Problems
Contests
National and Regional Contests
Serbia Contests
Serbia JBMO TST
2011 Serbia JBMO TST
4
4
Part of
2011 Serbia JBMO TST
Problems
(1)
minimum
Source:
11/24/2013
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
inequalities