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Dutch Mathematical Olympiad
2013 Dutch Mathematical Olympiad
2
3x3 system, x + y - z = -1 , x^2 - y^2 + z^2 = 1, - x^3 + y^3 + z^3 = -1
3x3 system, x + y - z = -1 , x^2 - y^2 + z^2 = 1, - x^3 + y^3 + z^3 = -1
Source: Dutch NMO 2013 p2
September 6, 2019
algebra
system of equations
Problem Statement
Find all triples
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of real numbers satisfying:
x
+
y
−
z
=
−
1
x + y - z = -1
x
+
y
−
z
=
−
1
,
x
2
−
y
2
+
z
2
=
1
x^2 - y^2 + z^2 = 1
x
2
−
y
2
+
z
2
=
1
and
−
x
3
+
y
3
+
z
3
=
−
1
- x^3 + y^3 + z^3 = -1
−
x
3
+
y
3
+
z
3
=
−
1
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