SOLUTION: The square of the first of three consecutive odd integers is 9 more than 6 times the sum of the second and third. Find the integers.

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Question 534852: The square of the first of three consecutive odd integers is 9 more than 6 times the sum of the second and third. Find the integers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 3 consecutive odd integers be
+n+, +n+%2B+2+, +n+%2B+4+
given:
+n%5E2+=+6%2A%28+n+%2B+2+%2B+n+%2B+4+%29+%2B+9+
+n%5E2+=+6%2A%28+2n+%2B+6+%29+%2B+9+
+n%5E2+=+12n+%2B+36+%2B+9+
+n%5E2+-+12n+-+45+=+0+
+%28+n+%2B+3+%29%2A%28+n+-+15+%29+=+0+
+n+=+15+
+n+%2B+2+=+17+
+n+%2B+4+=+19+
The numbers are 15, 17, and 19
check:
+n%5E2+=+6%2A%28+2n+%2B+6+%29+%2B+9+
+15%5E2+=+6%2A%28+2%2A15+%2B+6+%29+%2B+9+
+225+=+6%2A36+%2B+9+
+225+=+216+%2B+9+
+225+=+225+
OK