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Standard IX
Mathematics
Question
If
x
+
1
x
=
12
, then find the value of
(
x
2
+
1
x
2
)
.
Open in App
Solution
Verified by Toppr
Given,
x
+
1
x
=
12
.
We know,
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
.
Then,
(
x
+
1
x
)
2
=
144
⇒
x
2
+
1
x
2
+
2
×
x
×
1
x
=
144
⇒
x
2
+
1
x
2
+
2
=
144
⇒
x
2
+
1
x
2
=
144
−
2
⇒
x
2
+
1
x
2
=
142
.
Therefore, the required answer is
142
.
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