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Byju's Answer
Standard XII
Mathematics
Finding Integral Part of Numbers of the Form a^b Where a Is Irrational
If n is posit...
Question
If n is positive integer and
(
3
√
3
+
5
)
2
n
+
1
=
α
+
β
where
α
is an integer and
0
<
β
<
1
, then
A
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B
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C
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D
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Solution
The correct option is
A
α
+
β
=
(
3
√
3
−
5
)
2
n
+
1
β
1
=
(
3
√
3
−
5
)
2
n
+
1
,
w
h
e
r
e
β
1
<
1
⇒
α
+
β
+
β
1
=
e
v
e
n
i
n
t
e
g
e
r
,
β
+
β
1
=
.0
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0
Similar questions
Q.
If
n
is a positive integer and
(
3
√
3
+
5
)
2
n
+
1
=
α
+
β
where
α
is an integer and
0
<
β
<
1
, then
Q.
If
(
8
+
3
√
7
)
n
=
α
+
β
where
n
and
α
are positive integers and
β
is a positive proper fraction,then
Q.
Let
log
a
3
=
2
and
log
b
8
=
3.
If
α
=
[
log
a
b
]
+
1
,
where
[
.
]
denotes the greatest integer function and
β
is the integral part of
log
√
2
(
√
α
+
√
α
+
√
α
+
√
α
+
⋯
upto
∞
)
,
then
Q.
Let
α
and
β
be the roots of
x
2
+
x
+
1
=
0
. If
n
be positive integer, then
α
n
+
β
n
is
Q.
Let
log
a
3
=
2
and
log
b
8
=
3.
If
α
=
[
log
a
b
]
+
1
,
where
[
.
]
denotes the greatest integer function and
β
is the integral part of
log
√
2
(
√
α
+
√
α
+
√
α
+
√
α
+
⋯
upto
∞
)
,
then
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Standard XII Mathematics
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