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1992 Irish Math Olympiad
2
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Source: 1992 IrMO Paper 1 Problem 2
October 2, 2017
algebra
Problem Statement
How many ordered triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of real numbers satisfy the system of equations
x
2
+
y
2
+
z
2
=
9
,
x^2+y^2+z^2=9,
x
2
+
y
2
+
z
2
=
9
,
x
4
+
y
4
+
z
4
=
33
,
x^4+y^4+z^4=33,
x
4
+
y
4
+
z
4
=
33
,
x
y
z
=
ā
4
?
xyz=-4?
x
yz
=
ā
4
?
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