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IMO Longlists
1990 IMO Longlists
77
Three variables inequality - ILL 1990 ROM3
Three variables inequality - ILL 1990 ROM3
Source:
September 18, 2010
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
∈
R
a, b, c \in \mathbb R
a
,
b
,
c
∈
R
. Prove that
(
a
2
+
a
b
+
b
2
)
(
b
2
+
b
c
+
c
2
)
(
c
2
+
c
a
+
a
2
)
≥
(
a
b
+
b
c
+
c
a
)
3
.
(a^2 + ab + b^2)(b^2 + bc + c^2)(c^2 + ca + a^2) \geq (ab + bc + ca)^3.
(
a
2
+
ab
+
b
2
)
(
b
2
+
b
c
+
c
2
)
(
c
2
+
c
a
+
a
2
)
≥
(
ab
+
b
c
+
c
a
)
3
.
When does the equality hold?
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