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Balkan MO Shortlist
2014 Balkan MO Shortlist
A1
Balkan MO SL A1 easy
Balkan MO SL A1 easy
Source: Balkan MO SL 2014 A1
September 27, 2016
inequalities
Problem Statement
A1
\boxed{\text{A1}}
A1
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive reals numbers such that
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
.Prove that
2
(
a
2
+
b
2
+
c
2
)
≥
1
9
+
15
a
b
c
2(a^2+b^2+c^2)\ge \frac{1}{9}+15abc
2
(
a
2
+
b
2
+
c
2
)
≥
9
1
+
15
ab
c
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