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Baltic Way
2002 Baltic Way
2
2
Part of
2002 Baltic Way
Problems
(1)
One of a,b,c,d is not greater than -1
Source: Baltic Way 2002
11/13/2010
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be real numbers such that
a
+
b
+
c
+
d
=
−
2
a+b+c+d=-2
a
+
b
+
c
+
d
=
−
2
a
b
+
a
c
+
a
d
+
b
c
+
b
d
+
c
d
=
0
ab+ac+ad+bc+bd+cd=0
ab
+
a
c
+
a
d
+
b
c
+
b
d
+
c
d
=
0
Prove that at least one of the numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
is not greater than
−
1
-1
−
1
.
inequalities proposed
inequalities