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Junior Balkan MO
2015 Junior Balkan MO
2
Jbmo 2015 problem 2
Jbmo 2015 problem 2
Source:
June 26, 2015
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers such that
a
+
b
+
c
=
3
a+b+c = 3
a
+
b
+
c
=
3
. Find the minimum value of the expression
A
=
2
−
a
3
a
+
2
−
b
3
b
+
2
−
c
3
c
.
A=\dfrac{2-a^3}a+\dfrac{2-b^3}b+\dfrac{2-c^3}c.
A
=
a
2
−
a
3
+
b
2
−
b
3
+
c
2
−
c
3
.
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