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Nordic
2006 Nordic
2
Nordic MC 2006 Q2
Nordic MC 2006 Q2
Source:
March 3, 2013
quadratics
algebra
algebra unsolved
Problem Statement
Real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
are not all equal and satisfy
x
+
1
y
=
y
+
1
z
=
z
+
1
x
=
k
x+\frac{1}{y} = y + \frac{1}{z} = z + \frac{1}{x}=k
x
+
y
1
=
y
+
z
1
=
z
+
x
1
=
k
. Find all possible values of
k
k
k
.
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