SOLUTION: What are two odd consecutive numbers that have a product of 12,099

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Question 650340: What are two odd consecutive numbers that have a product of 12,099
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be +n+ and +n+%2B+2+
given:
+n%2A%28+n%2B2+%29+=+12099+
complete the square
+n%5E2+%2B+2n+%2B+%282%2F2%29%5E2+=+12099+%2B+%282%2F2%29%5E2+
+n%5E2+%2B+2n+%2B+1+=+12099+%2B+1+
+n%5E2+%2B+2n+%2B+1+=+12100+
+%28+n+%2B+1+%29%5E2+=+110%5E2+
+n+%2B+1+=+110+
+n+=+109+
+n+%2B+2+=+111+
The number are 109 and 111
check:
+109%2A111+=+12099+
+12099+=+12099+
OK