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Mathematics
Problem
If
x
2
+
x
+
1
=
0
x^2 + x + 1 = 0
x
2
+
x
+
1
=
0
find value of
(
x
+
1
x
)
3
+
(
x
2
+
1
x
2
)
3
+
⋯
+
(
x
100
+
1
x
100
)
3
\left(x + \frac{1}{x}\right)^3 + \left(x^2 + \frac{1}{x^2}\right)^3 + \dots + \left(x^{100} + \frac{1}{x^{100}}\right)^3
(
x
+
x
1
)
3
+
(
x
2
+
x
2
1
)
3
+
⋯
+
(
x
100
+
x
100
1
)
3
.
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