If x^2 + 1/x^2 = 11 , then find x - 1/x =?
Answers
Answered by
2
x
4
+
1
x
4
=
14159
Explanation:
As per the question, we have
x
+
1
x
=
11
∴
(
x
+
1
x
)
2
=
(
11
)
2
... [Squaring both sides]
∴
x
2
+
1
x
2
+
2
(
x
)
(
1
x
)
=
121
∴
x
2
+
1
x
2
+
2
(
x
)
(
1
x
)
=
121
∴
x
2
+
1
x
2
+
2
=
121
∴
x
2
+
1
x
2
=
121
−
2
=
119
... (i)
Now, back to
x
+
1
x
=
11
(
x
+
1
x
)
4
=
(
11
)
4
∴
x
4
+
1
x
4
+
4
(
x
3
)
(
1
x
)
+
6
(
x
2
)
(
1
x
2
)
+
4
(
x
)
(
1
x
3
)
=
(
11
)
4
∴
x
4
+
1
x
4
+
4
(
x
2
)
+
6
+
4
(
1
x
2
)
=
14641
∴
x
4
+
1
x
4
+
4
(
x
2
)
+
4
(
1
x
2
)
=
14641
−
6
∴
x
4
+
1
x
4
+
4
(
x
2
+
1
x
2
)
=
14635
∴
x
4
+
1
x
4
+
4
(
119
)
=
14635
... [Substituting the value of
x
2
+
1
x
2
from (i)]
∴
x
4
+
1
x
4
+
476
=
14635
∴
x
4
+
1
x
4
=
14635
−
476
∴
x
4
+
1
x
4
=
14159
Hence, the answer.
Note: If you want to know more about the identity
(
a
+
b
)
4
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