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AZE JBMO TST
AZE JBMO TST
Source: AZE JBMO TST
May 2, 2015
three variable inequality
Inequality
Problem Statement
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
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