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2016 IberoAmerican
2
Iberoamerican 2016 problem $2$
Iberoamerican 2016 problem $2$
Source:
September 27, 2016
contests
Iberoamerican
algebra
Iberoamerican 2016
Problem Statement
Find all positive real numbers
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
such that:
x
=
1
y
2
+
y
−
1
x = \frac{1}{y^2+y-1}
x
=
y
2
+
y
−
1
1
y
=
1
z
2
+
z
−
1
y = \frac{1}{z^2+z-1}
y
=
z
2
+
z
−
1
1
z
=
1
x
2
+
x
−
1
z = \frac{1}{x^2+x-1}
z
=
x
2
+
x
−
1
1
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