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Mathematics
Mathematics
Problem
If
α
,
β
\alpha, \beta
α
,
β
are the roots of the equation,
x
2
−
x
−
1
=
0
x^2 - x - 1 = 0
x
2
−
x
−
1
=
0
and
S
n
=
2023
α
n
+
2024
β
n
S_n = 2023\alpha^n + 2024\beta^n
S
n
=
2023
α
n
+
2024
β
n
, then (A)
2
S
12
=
S
11
+
S
10
2S_{12} = S_{11} + S_{10}
2
S
12
=
S
11
+
S
10
(B)
S
12
=
S
11
+
S
10
S_{12} = S_{11} + S_{10}
S
12
=
S
11
+
S
10
(C)
2
S
11
=
S
12
+
S
10
2S_{11} = S_{12} + S_{10}
2
S
11
=
S
12
+
S
10
(D)
S
11
=
S
10
+
S
12
S_{11} = S_{10} + S_{12}
S
11
=
S
10
+
S
12
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