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2013 JBMO Shortlist
1
Equation
Equation
Source: JBMO 2013 Shortlist
April 24, 2016
algebra
Problem Statement
A
1
\boxed{A1}
A
1
Find all ordered triplets of
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
real numbers that satisfy the following system of equation
x
3
=
z
y
−
2
y
z
x^3=\frac{z}{y}-\frac {2y}{z}
x
3
=
y
z
−
z
2
y
y
3
=
x
z
−
2
z
x
y^3=\frac{x}{z}-\frac{2z}{x}
y
3
=
z
x
−
x
2
z
z
3
=
y
x
−
2
x
y
z^3=\frac{y}{x}-\frac{2x}{y}
z
3
=
x
y
−
y
2
x
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