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UPSC CDS Math Quadratic Equations and Inequations Questions
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© examsnet.com
Question : 2
Total: 67
The sum of the squares of four consecutive natural numbers is 294.What is the sum of the numbers?
[2019 CDS-II]
38
34
30
26
Validate
Solution:
(
n
−
1
)
2
+
n
2
+
(
n
+
1
)
2
+
(
n
+
2
)
2
=
294
n
2
+
1
−
2
n
+
n
2
+
n
2
+
1
+
2
n
+
n
2
+
4
n
+
4
=
294
4
n
2
+
4
n
+
6
=
294
4
n
2
+
4
n
−
288
=
0
n
2
+
n
−
77
=
0
n
2
+
9
n
−
8
n
−
72
=
0
⇒
(
n
−
8
)
(
n
+
9
)
=
0
⇒
∴
n
=
8
,
−
9
∴
number are
7
,
8
,
9
,
10
Sum of number
=
7
+
8
+
9
+
10
=
34
© examsnet.com
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