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Standard XII
Mathematics
Question
If
x
−
1
x
=
9
, find the value of
x
2
+
1
x
2
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Solution
Verified by Toppr
We have,
x
−
1
x
=
9
On squaring both sides, we get
(
x
−
1
x
)
2
=
9
2
⇒
x
2
−
2
×
x
×
1
x
+
(
1
x
)
2
=
81
⇒
x
2
−
2
+
(
1
x
)
2
=
81
⇒
x
2
+
1
x
2
=
81
+
2
[On transposing -2 on RHS]
⇒
x
2
+
1
x
2
=
83
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