SOLUTION: Find 3 consecutive odd numbers where the product of the smaller two numbers is 34 less than the square of the largest number.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find 3 consecutive odd numbers where the product of the smaller two numbers is 34 less than the square of the largest number.      Log On


   



Question 1045078: Find 3 consecutive odd numbers where the product of the smaller two numbers is 34 less than the square of the largest number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 3 consecutive odd numbers be
+n+, +n+%2B+2+, and +n+%2B+4+
------------------------------
+n%2A%28+n+%2B+2+%29+=+%28+n+%2B+4+%29%5E2+-+34++
+n%5E2+%2B+2n+=+n%5E2+%2B+8n+%2B+16+-+34+
+2n+=+8n+-+18+
+6n+=+18+
+n+=+3+
and
+n+%2B+2+=+5+
+n+%2B+4+=+7+
----------------
The numbers are 3, 5, and 7
check:
+n%2A%28+n+%2B+2+%29+=+%28+n+%2B+4+%29%5E2+-+34++
+3%2A%28+3+%2B+2+%29+=+%28+3+%2B+4+%29%5E2+-+34++
+3%2A5+=+7%5E2+-+34+
+15+=49+-+34+
+15+=+15+
OK