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Standard IX
Mathematics
Question
If
x
=
5
−
2
√
6
,
find
x
2
+
1
x
2
.
Open in App
Solution
Verified by Toppr
We know,
x
2
+
1
x
2
=
(
x
−
1
x
)
2
+
2
Given,
x
=
5
−
2
√
6
.
Then,
1
x
=
1
5
−
2
√
6
=
5
+
2
√
6
(
5
−
2
√
6
)
(
5
+
2
√
6
)
=
5
+
2
√
6
5
2
−
(
2
√
6
)
2
=
5
+
2
√
6
25
−
24
=
5
+
2
√
6
1
=
5
+
2
√
6
.
Then,
x
2
+
1
x
=
(
5
−
2
√
6
−
(
5
+
2
√
6
)
)
2
+
2
∴
(
−
4
√
6
)
2
+
2
=
96
+
2
=
98
.
Therefore, the required value is
98
.
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