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5
2010 Algebra #5: Symmetrical Powers
2010 Algebra #5: Symmetrical Powers
Source:
July 15, 2012
complex numbers
Problem Statement
Suppose that
x
x
x
and
y
y
y
are complex numbers such that
x
+
y
=
1
x+y=1
x
+
y
=
1
and
x
20
+
y
20
=
20
x^{20}+y^{20}=20
x
20
+
y
20
=
20
. Find the sum of all possible values of
x
2
+
y
2
x^2+y^2
x
2
+
y
2
.
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