MathDB
Problems
Contests
International Contests
Junior Balkan MO
2015 Junior Balkan MO
2
2
Part of
2015 Junior Balkan MO
Problems
(1)
Jbmo 2015 problem 2
Source:
6/26/2015
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
.
inequalities