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Problems
Contests
National and Regional Contests
Germany Contests
German National Olympiad
1997 German National Olympiad
4
4
Part of
1997 German National Olympiad
Problems
(1)
x^3 = 2y-1, y^3 = 2z-1, z^3 = 2x-1
Source: Germany 1997 p4
2/22/2020
Find all real solutions
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of the system of equations
{
x
3
=
2
y
−
1
y
3
=
2
z
−
1
z
3
=
2
x
−
1
\begin{cases} x^3 = 2y-1 \\y^3 = 2z-1\\ z^3 = 2x-1\end{cases}
⎩
⎨
⎧
x
3
=
2
y
−
1
y
3
=
2
z
−
1
z
3
=
2
x
−
1
system of equations
algebra