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Bulgaria JBMO Team Selection Test
2023 Bulgaria JBMO TST
1
1
Part of
2023 Bulgaria JBMO TST
Problems
(1)
Some training in systems of equations
Source: Bulgaria JBMO TST 2023, Day 2, Problem 1
6/17/2023
Determine all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of real numbers such that
x
4
+
y
3
z
=
z
x
x^4 + y^3z = zx
x
4
+
y
3
z
=
z
x
,
y
4
+
z
3
x
=
x
y
y^4 + z^3x = xy
y
4
+
z
3
x
=
x
y
and
z
4
+
x
3
y
=
y
z
z^4 + x^3y = yz
z
4
+
x
3
y
=
yz
.
algebra
system of equations
Algebraic Manipulations