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UPSC 2013 CDS 2 Math Paper
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© examsnet.com
Question : 3
Total: 100
Which one is one of the factors of
x
2
+
1
x
2
+
8
(
x
+
1
x
)
+
14
?
[2013 CDS-II]
x
+
1
x
+
1
x
+
1
x
+
3
x
+
1
x
+
6
x
+
1
x
+
7
Validate
Solution:
(
x
+
1
x
)
2
+
8
(
x
+
1
x
)
+
12
⇒
y
2
+
8
y
+
12
=
0
,
where
(
x
+
1
x
)
=
y
Factorizing
y
2
+
8
y
+
12
=
0
,we get
y
2
+
6
y
+
2
y
+
12
=
0
⇒
y
(
y
+
6
)
+
2
(
y
+
6
)
=
0
⇒
(
y
+
2
)
(
y
+
6
)
=
0
,So,
(
x
+
1
x
+
2
)
and
(
x
+
1
x
+
6
)
are the factors of the given expression
© examsnet.com
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