SOLUTION: Find two consecutive positive integers such that the sum of their squares is 145.

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Question 674341: Find two consecutive positive integers such that the sum of their squares is 145.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the consecutive integers be +n+ and +n+%2B+1+
given:
+n%5E2+%2B+%28+n+%2B+1+%29%5E2++=+145+
+n%5E2+%2B+n%5E2+%2B+2n+%2B+1+=+145+
+2n%5E2+%2B+2n+-+144+=+0+
+n%5E2+%2B+n+-+72+=+0+
I can see that this is
+%28+n+%2B+9+%29%2A%28+n+-+8+%29+=+0+
+n+=+8+ is the positive answer
+n+%2B+1+=+9+
The numbers are 8 and 9
check:
+8%5E2+%2B+9%5E2+=+64+%2B+81+
+64+%2B+81+=+145+
OK