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2012 Benelux
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Part of
2012 Benelux
Problems
(1)
Quadruples (a,b,c,d) with abcd=1
Source: Benelux Mathematical Olympiad 2012
4/23/2012
Find all quadruples
(
a
,
b
,
c
,
d
)
(a,b,c,d)
(
a
,
b
,
c
,
d
)
of positive real numbers such that
a
b
c
d
=
1
,
a
2012
+
2012
b
=
2012
c
+
d
2012
abcd=1,a^{2012}+2012b=2012c+d^{2012}
ab
c
d
=
1
,
a
2012
+
2012
b
=
2012
c
+
d
2012
and
2012
a
+
b
2012
=
c
2012
+
2012
d
2012a+b^{2012}=c^{2012}+2012d
2012
a
+
b
2012
=
c
2012
+
2012
d
.
inequalities
algebra proposed
algebra