MathDB
Problems
Contests
International Contests
JBMO ShortLists
2014 JBMO Shortlist
7
7
Part of
2014 JBMO Shortlist
Problems
(1)
AZE JBMO TST
Source: AZE JBMO TST
5/2/2015
a
,
b
,
c
∈
R
+
a,b,c\in\mathbb{R^+}
a
,
b
,
c
∈
R
+
and
a
2
+
b
2
+
c
2
=
48
a^2+b^2+c^2=48
a
2
+
b
2
+
c
2
=
48
. Prove that
a
2
2
b
3
+
16
+
b
2
2
c
3
+
16
+
c
2
2
a
3
+
16
≤
2
4
2
a^2\sqrt{2b^3+16}+b^2\sqrt{2c^3+16}+c^2\sqrt{2a^3+16}\le24^2
a
2
2
b
3
+
16
+
b
2
2
c
3
+
16
+
c
2
2
a
3
+
16
≤
2
4
2
three variable inequality
Inequality