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National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2016 Dutch BxMO TST
2
2
Part of
2016 Dutch BxMO TST
Problems
(1)
system x^2 - y = (z - 1)^2, y^2 - z = (x - 1)^2, z^2 - x = (y -1)^2
Source: Dutch BxMO TST 2016 p2
8/24/2019
Determine all triples (x, y, z) of non-negative real numbers that satisfy the following system of equations
{
x
2
−
y
=
(
z
−
1
)
2
y
2
−
z
=
(
x
−
1
)
2
z
2
−
x
=
(
y
−
1
)
2
\begin{cases} x^2 - y = (z - 1)^2\\ y^2 - z = (x - 1)^2 \\ z^2 - x = (y -1)^2 \end{cases}
⎩
⎨
⎧
x
2
−
y
=
(
z
−
1
)
2
y
2
−
z
=
(
x
−
1
)
2
z
2
−
x
=
(
y
−
1
)
2
.
algebra
system of equations