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2022 Thailand Online MO
1
x^3+y+z=x+y^3+z=x+y+z^3=-xyz
x^3+y+z=x+y^3+z=x+y+z^3=-xyz
Source: 2022 Thailand Online MO P1
April 4, 2022
algebra
equation
Problem Statement
Determine, with proof, all triples of real numbers
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
satisfying the equations
x
3
+
y
+
z
=
x
+
y
3
+
z
=
x
+
y
+
z
3
=
ā
x
y
z
.
x^3+y+z=x+y^3+z=x+y+z^3=-xyz.
x
3
+
y
+
z
=
x
+
y
3
+
z
=
x
+
y
+
z
3
=
ā
x
yz
.
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