The sum of squares of five consecutive natural numbers in 1455.find them.
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Answer:
Solution
Let the five consecutive integers be
n
,
n
+
1
,
n
+
2
,
n
+
3
,
n
+
4
then,
n
2
+
(
n
+
1
)
2
+
(
n
+
2
)
2
+
(
n
+
3
)
2
+
(
n
+
4
)
2
=
1455
5
n
2
+
20
n
+
30
−
1455
=
0
5
n
2
+
20
n
−
1425
=
0
n
2
+
4
n
−
285
=
0
n
=
−
4
±
√
16
+
1140
2
=
−
4
±
34
2
=
15
,
−
17
Hence, the numbers are
15
,
16
,
17
,
18
,
19
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