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Byju's Answer
Standard XI
Mathematics
nth Root of a Complex Number
If the value ...
Question
If the value of
a
+
1
a
=
3
, then the value of
a
4
+
1
a
4
is equal to
.
A
51
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B
47
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C
45
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D
49
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Solution
The correct option is
B
47
It is given that
a
+
1
a
=
3
Using identity,
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
,
we have
a
2
+
1
a
2
=
(
a
+
1
a
)
2
−
2
⇒
a
2
+
1
a
2
=
3
2
−
2
⇒
a
2
+
1
a
2
=
9
−
2
⇒
a
2
+
1
a
2
=
7
Squaring both sides we get,
(
a
2
+
1
a
2
)
2
=
7
2
⇒
(
a
2
)
2
+
(
1
a
2
)
2
+
2
(
a
2
)
(
1
a
2
)
=
7
2
⇒
a
4
+
1
a
4
+
2
=
49
⇒
a
4
+
1
a
4
=
47
Suggest Corrections
10
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