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Byju's Answer
Standard VIII
Mathematics
Finding Square Root through Repeated Subtraction
If x + 1x =...
Question
If
x
+
1
x
=
5
, find the value of
x
4
+
1
x
4
.
A
144
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B
400
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C
236
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D
527
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Solution
The correct option is
A
527
Given
x
+
1
x
=
5
let
y
=
x
4
+
1
x
4
x
+
1
x
=
5
Squaring on both sides
(
x
+
1
x
)
2
=
5
2
⇒
x
2
+
1
x
2
+
2
(
x
)
(
1
x
)
=
25
⇒
x
2
+
1
x
2
+
2
=
25
⇒
x
2
+
1
x
2
=
23
Squaring on both sides
⇒
(
x
2
+
1
x
2
)
2
=
23
2
⇒
x
4
+
1
x
4
)
+
2
(
x
2
)
(
1
x
2
)
=
529
⇒
x
4
+
1
x
4
+
2
=
529
⇒
x
4
+
1
x
4
=
527
⇒
y
=
527
Thus, required term value is
527
.
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