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1
Find a^8 + b^8 + c^8, if a, b, c are roots of x^3 - x + 1 = 0
Find a^8 + b^8 + c^8, if a, b, c are roots of x^3 - x + 1 = 0
Source: Vietnamese MO (VMO) 1975 P1
August 20, 2018
algebra
polynomial
polynomial equation
Problem Statement
The roots of the equation
x
3
ā
x
+
1
=
0
x^3 - x + 1 = 0
x
3
ā
x
+
1
=
0
are
a
,
b
,
c
a, b, c
a
,
b
,
c
. Find
a
8
+
b
8
+
c
8
a^8 + b^8 + c^8
a
8
+
b
8
+
c
8
.
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