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Dutch BxMO/EGMO TST
2021 Dutch BxMO TST
2
x^2- yz = |y-z| +1, y^2 - zx = |z-x| +1, z^2 -xy = |x-y| + 1
x^2- yz = |y-z| +1, y^2 - zx = |z-x| +1, z^2 -xy = |x-y| + 1
Source: 2021 Dutch BxMO TST p2
December 28, 2021
system of equations
System
algebra
Problem Statement
Find all triplets
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of real numbers for which
{
x
2
−
y
z
=
∣
y
−
z
∣
+
1
y
2
−
z
x
=
∣
z
−
x
∣
+
1
z
2
−
x
y
=
∣
x
−
y
∣
+
1
\begin{cases}x^2- yz = |y-z| +1 \\ y^2 - zx = |z-x| +1 \\ z^2 -xy = |x-y| + 1 \end{cases}
⎩
⎨
⎧
x
2
−
yz
=
∣
y
−
z
∣
+
1
y
2
−
z
x
=
∣
z
−
x
∣
+
1
z
2
−
x
y
=
∣
x
−
y
∣
+
1
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