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Akdeniz University MO
2011 Akdeniz University MO
3
inequality...
inequality...
Source:
January 29, 2016
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
positive reals such that
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
. Show that following expression's minimum value is
2
2
2
.
a
+
b
+
c
a
b
+
b
c
+
c
a
+
1
1
+
2
a
b
+
1
1
+
2
b
c
+
1
1
+
2
c
a
\frac{\sqrt a +\sqrt b +\sqrt c}{ab+bc+ca} + \frac{1}{1+2\sqrt {ab}} + \frac {1}{1+ 2\sqrt {bc}} + \frac{1}{1+ 2\sqrt {ca}}
ab
+
b
c
+
c
a
a
+
b
+
c
+
1
+
2
ab
1
+
1
+
2
b
c
1
+
1
+
2
c
a
1
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