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National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2011 Dutch BxMO TST
3
3
Part of
2011 Dutch BxMO TST
Problems
(1)
x^2 + y^2 + z^2 + 1 = xy + yz + zx +|x - 2y + z| equation in R^3
Source: Dutch BxMO TST2011 p3
8/24/2019
Find all triples
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of real numbers that satisfy
x
2
+
y
2
+
z
2
+
1
=
x
y
+
y
z
+
z
x
+
∣
x
−
2
y
+
z
∣
x^2 + y^2 + z^2 + 1 = xy + yz + zx +|x - 2y + z|
x
2
+
y
2
+
z
2
+
1
=
x
y
+
yz
+
z
x
+
∣
x
−
2
y
+
z
∣
.
absolute value
equation
algebra