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UPSC 2015 CDS II Math Paper
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© examsnet.com
Question : 4
Total: 100
What is
√
4
+
√
4
−
√
4
+
√
4
−
.
.
.
.
.
.
.
.
.
.
.
.
.
equal to ?
[2015 CDS-II]
3
√
13
−
1
2
√
13
+
1
2
0
None of Above
Validate
Solution:
x
=
√
4
+
√
4
−
√
4
+
√
4
−
.
.
.
.
.
.
.
.
.
.
.
.
.
⇒
x
2
=
4
+
√
4
−
x
⇒
(
x
2
−
4
)
2
+
x
=
4
.....(1)
x
=
3
and
x
=
0
does not satisfy (1).
When
x
=
√
13
−
1
2
(
x
2
−
4
)
2
+
x
=
(
13
+
1
−
2
√
13
4
−
4
)
2
+
√
13
−
1
2
=
(
√
13
+
1
2
)
2
+
√
13
−
1
2
=
3
+
√
13
≠
4
So,
x
=
√
13
−
1
2
does not satisfy (1).
When
x
=
√
13
+
1
2
,
(
x
2
−
4
)
2
+
x
=
(
13
+
1
+
2
√
13
4
−
4
)
2
+
√
13
+
1
2
=
(
√
13
−
1
2
)
2
+
√
13
+
1
2
=
4
So,
x
=
√
13
+
1
2
satisfy (1).
∴
√
4
+
√
4
−
√
4
+
√
4
−
.
.
.
.
.
.
=
√
13
+
1
2
© examsnet.com
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