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UPSC CDS Math Square, Roots and Surds Questions
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© examsnet.com
Question : 4
Total: 22
Suppose n is a positive integer such that (
n
2
+ 48) is a perfect square. What is the number of such n ?
[2019 CDS-I]
One
Two
Three
Four
Validate
Solution:
n
2
+
48
=
x
2
x
2
−
n
2
=
48
(
x
+
n
)
(
x
−
n
)
=
48
Thus, we have:
x
+
n
=
24
,
x
−
n
=
2
x
+
n
=
12
,
x
−
n
=
4
x
+
n
=
8
,
x
−
n
=
6
Since integral values are allowed, therefore, we cannot use odd values for (x + n) or (x – n).
∴ Three values of n are possible.
© examsnet.com
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