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13
2013 PUMaC Team 13
2013 PUMaC Team 13
Source:
November 24, 2013
Problem Statement
The equation
x
5
−
2
x
4
−
1
=
0
x^5-2x^4-1=0
x
5
−
2
x
4
−
1
=
0
has five complex roots
r
1
,
r
2
,
r
3
,
r
4
,
r
5
r_1,r_2,r_3,r_4,r_5
r
1
,
r
2
,
r
3
,
r
4
,
r
5
. Find the value of
1
r
1
8
+
1
r
2
8
+
1
r
3
8
+
1
r
4
8
+
1
r
5
8
.
\dfrac1{r_1^8}+\dfrac1{r_2^8}+\dfrac1{r_3^8}+\dfrac1{r_4^8}+\dfrac1{r_5^8}.
r
1
8
1
+
r
2
8
1
+
r
3
8
1
+
r
4
8
1
+
r
5
8
1
.
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