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Problem
Problem
Let
α
\alpha
α
and
β
\beta
β
be the roots of
x
2
−
6
x
−
2
=
0
x^2 - 6x - 2 = 0
x
2
−
6
x
−
2
=
0
, with
α
>
β
\alpha > \beta
α
>
β
. If
a
n
=
α
n
−
β
n
a_n = \alpha^n - \beta^n
a
n
=
α
n
−
β
n
for
n
≥
1
n \ge 1
n
≥
1
, find the value of
a
10
−
2
a
8
2
a
9
\frac{a_{10} - 2a_8}{2a_9}
2
a
9
a
10
−
2
a
8
. a. 1 b. 2 c. 3 d. 4
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