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Mathematics
Mathematics
Problem
Let
α
\alpha
α
and
β
\beta
β
be the roots of the equation,
5
x
2
+
6
x
−
2
=
0.
If
S
n
=
α
n
+
β
n
,
5x^2 + 6x - 2 = 0. \text{ If } S_n = \alpha^n + \beta^n,
5
x
2
+
6
x
−
2
=
0.
If
S
n
=
α
n
+
β
n
,
n
=
1
,
2
,
3
,
…
n = 1, 2, 3, \dots
n
=
1
,
2
,
3
,
…
then (a)
5
S
6
+
6
S
5
+
2
S
4
=
0
5S_6 + 6S_5 + 2S_4 = 0
5
S
6
+
6
S
5
+
2
S
4
=
0
(b)
6
S
6
+
5
S
5
+
2
S
4
=
0
6S_6 + 5S_5 + 2S_4 = 0
6
S
6
+
5
S
5
+
2
S
4
=
0
(c)
6
S
6
+
5
S
5
=
2
S
4
6S_6 + 5S_5 = 2S_4
6
S
6
+
5
S
5
=
2
S
4
(d)
5
S
6
+
6
S
5
=
2
S
4
5S_6 + 6S_5 = 2S_4
5
S
6
+
6
S
5
=
2
S
4
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