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APMO
2004 APMO
5
Not homogenous
Not homogenous
Source: APMO 2004
March 23, 2004
inequalities
algebra
APMO
Problem Statement
Prove that the inequality
(
a
2
+
2
)
(
b
2
+
2
)
(
c
2
+
2
)
≥
9
(
a
b
+
b
c
+
c
a
)
\left(a^{2}+2\right)\left(b^{2}+2\right)\left(c^{2}+2\right) \geq 9\left(ab+bc+ca\right)
(
a
2
+
2
)
(
b
2
+
2
)
(
c
2
+
2
)
≥
9
(
ab
+
b
c
+
c
a
)
holds for all positive reals
a
a
a
,
b
b
b
,
c
c
c
.
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