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UPSC 2016 CDS II Math Paper
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© examsnet.com
Question : 9
Total: 100
The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number. then what is the difference of the larger and smaller numbers ?
[2016 CDS-II]
2
3
4
6
Validate
Solution:
Let the two positive integers be x and y (x > y).
∴
x
2
=
18
y
.....(a)
Also
x
2
+
y
2
=
208
.....(b)
From (a) and (b), we have
y
2
+
18
y
−
208
=
0
⇒
(
y
+
26
)
(
y
−
8
)
=
0
⇒
y
=
8
(
y
>
0
)
∴
x
2
=
18
×
8
=
144
⇒
x
=
12
(
x
>
0
)
Difference of the larger and smaller numbers
=
12
−
8
=
4
© examsnet.com
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