Can 5 consecutive triangular numbers greater than 15 . From these number consider two consecutive numbers and examine whether their sums are square numbers or not
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Can 5 consecutive triangular numbers greater than 15 . From these number consider two consecutive numbers and examine whether their sums are square numbers or not
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Answer:
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
5n
2
+20n+30−1455=0
5n
2
+20n−1425=0
n
2
+4n−285=0
n=
2
−4±
16+1140
=
2
−4±34
=15,−17
Hence, the numbers are 15,16,17,18,19
Answer:
Hope u r satisfied with this :-)))))))
Step-by-step explanation:
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
5n
2
+20n+30−1455=0
5n
2
+20n−1425=0
n
2
+4n−285=0
n=
2
−4±
16+1140
=
2
−4±34
=15,−17
Hence, the numbers are 15,16,17,18,19