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UPSC CDS I 2019 Math Paper
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© examsnet.com
Question : 41
Total: 100
What is the value of 2 +
√
2
+
√
2
+
√
.
.
.
.
.
.
.
.
.
?
[2019 CDS-I]
1
2
3
4
Validate
Solution:
Let
x
=
2
+
√
2
+
√
2
+
√
.
.
.
.
.
.
.
⇒
x
−
2
=
√
2
+
√
2
√
.
.
.
.
.
.
.
.
⇒
(
x
−
2
)
2
=
2
+
√
2
+
√
.
.
.
.
.
⇒
x
2
−
4
x
+
4
=
x
⇒
x
2
−
5
x
+
4
=
0
⇒
(
x
−
4
)
(
x
−
1
)
=
0
⇒
x
=
4
or
x
=
1
Since the given expression is greater than 2, therefore, x = 4
© examsnet.com
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