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6
2000 HMMT RMT Team #6
2000 HMMT RMT Team #6
Source:
March 8, 2024
algebra
Problem Statement
If
a
a
a
is a root of
x
3
−
x
−
1
=
0
x^3-x-1 = 0
x
3
−
x
−
1
=
0
, compute the value of
a
10
+
2
a
8
−
a
7
−
3
a
6
−
3
a
5
+
4
a
4
+
2
a
3
−
4
a
4
−
6
a
−
17.
a^{10 }+ 2a^8 -a^7 - 3a^6 - 3a^5 + 4a^4 + 2a^3 - 4a^4 - 6a - 17.
a
10
+
2
a
8
−
a
7
−
3
a
6
−
3
a
5
+
4
a
4
+
2
a
3
−
4
a
4
−
6
a
−
17.
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