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1972 IMO Longlists
2
2
Part of
1972 IMO Longlists
Problems
(1)
System of equations with at most one real solution
Source:
11/2/2010
Find all real values of the parameter
a
a
a
for which the system of equations
x
4
=
y
z
−
x
2
+
a
,
x^4 = yz - x^2 + a,
x
4
=
yz
−
x
2
+
a
,
y
4
=
z
x
−
y
2
+
a
,
y^4 = zx - y^2 + a,
y
4
=
z
x
−
y
2
+
a
,
z
4
=
x
y
−
z
2
+
a
,
z^4 = xy - z^2 + a,
z
4
=
x
y
−
z
2
+
a
,
has at most one real solution.
parameterization
algebra
system of equations
algebra unsolved