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2019 Centroamerican and Caribbean Math Olympiad
5
2019 Central American and Caribbean Mathematical Olympiad, P5
2019 Central American and Caribbean Mathematical Olympiad, P5
Source:
June 19, 2019
algebra
inequalities
Problem Statement
Let
a
,
b
a,\ b
a
,
b
and
c
c
c
be positive real numbers so that
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
. Show that
a
a
2
+
6
b
c
+
b
b
2
+
6
a
c
+
c
c
2
+
6
a
b
≤
3
2
4
a\sqrt{a^2+6bc}+b\sqrt{b^2+6ac}+c\sqrt{c^2+6ab}\leq\frac{3\sqrt{2}}{4}
a
a
2
+
6
b
c
+
b
b
2
+
6
a
c
+
c
c
2
+
6
ab
≤
4
3
2
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