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Mathematics
Mathematics
Problem
If
α
,
β
≠
0
\alpha, \beta \ne 0
α
,
β
=
0
and
f
(
n
)
=
α
n
+
β
n
f(n) = \alpha^n + \beta^n
f
(
n
)
=
α
n
+
β
n
and
∣
3
1
+
f
(
1
)
1
+
f
(
2
)
1
+
f
(
1
)
1
+
f
(
2
)
1
+
f
(
3
)
1
+
f
(
2
)
1
+
f
(
3
)
1
+
f
(
4
)
∣
=
k
(
1
−
α
)
2
(
1
−
β
)
2
(
α
−
β
)
2
,
\left|\begin{matrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4) \end{matrix}\right| = k(1-\alpha)^2(1-\beta)^2(\alpha-\beta)^2,
3
1
+
f
(
1
)
1
+
f
(
2
)
1
+
f
(
1
)
1
+
f
(
2
)
1
+
f
(
3
)
1
+
f
(
2
)
1
+
f
(
3
)
1
+
f
(
4
)
=
k
(
1
−
α
)
2
(
1
−
β
)
2
(
α
−
β
)
2
,
then
k
k
k
is equal to a. 1 b. -1 c.
α
β
\alpha\beta
α
β
d.
1
/
α
β
1/\alpha\beta
1/
α
β
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