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USAMO
2001
Problem - 3597
Let
a
,
b
,
c
≥
0
and satisfy
a
2
+
b
2
+
c
2
+
a
b
c
=
4
.
Show that
0
≤
a
b
+
b
c
+
c
a
−
a
b
c
≤
2.
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