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District Olympiad
2004 District Olympiad
1
Easy inequality.
Easy inequality.
Source: Kyrgyz TST 2005.(also Romanian olympiad)
April 20, 2005
Problem Statement
If reals
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfy
a
2
+
b
2
+
c
2
=
3
a^2+b^2+c^2=3
a
2
+
b
2
+
c
2
=
3
then prove that
∣
a
∣
+
∣
b
∣
+
∣
c
∣
−
a
b
c
≤
4
|a|+|b|+|c|-abc\leq4
∣
a
∣
+
∣
b
∣
+
∣
c
∣
−
ab
c
≤
4
.
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