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UPSC 2015 CDS II Math Paper
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© examsnet.com
Question : 8
Total: 100
If
x
=
√
3
+
√
2
, then the value of
x
3
+
x
+
1
x
+
1
x
3
is
[2015 CDS-II]
10
√
3
20
√
3
10
√
2
20
√
2
Validate
Solution:
x
=
√
3
+
√
2
⇒
1
x
=
1
√
3
+
√
2
=
1
√
3
+
√
2
×
√
3
−
√
2
√
3
−
√
2
=
√
3
−
√
2
⇒
x
+
1
x
=
2
√
3
⇒
(
x
+
1
x
)
2
=
(
2
√
3
)
2
⇒
x
2
+
1
x
2
+
2
=
12
⇒
x
2
+
1
x
2
=
12
−
2
=
10
x
3
+
1
x
3
=
(
x
+
1
x
)
(
x
2
+
1
x
2
−
1
)
=
2
√
3
×
(
10
−
1
)
=
18
√
3
∴
x
3
+
x
+
1
x
+
1
x
3
=
x
3
+
1
x
3
+
x
+
1
x
=
18
√
3
+
2
√
3
=
20
√
3
© examsnet.com
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