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5
3x3 system x^2 - y = (z -1)^2 (Chile 2016 L2 P5)
3x3 system x^2 - y = (z -1)^2 (Chile 2016 L2 P5)
Source:
October 22, 2022
algebra
system of equations
Problem Statement
Determine all triples
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of nonnegative real numbers that verify the following system of equations:
x
2
−
y
=
(
z
−
1
)
2
x^2 - y = (z -1)^2
x
2
−
y
=
(
z
−
1
)
2
y
2
−
z
=
(
x
−
1
)
2
y^2 - z = (x -1)^2
y
2
−
z
=
(
x
−
1
)
2
z
2
−
x
=
(
y
−
1
)
2
z^2 - x = (y - 1)^2
z
2
−
x
=
(
y
−
1
)
2
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