SOLUTION: Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbers.

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Question 263542: Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A way to guarantee that a number will be odd is to call it
2n+%2B+1
Odd integers skip every other number, so I can
call them 2n%2B1,2n%2B3,2n%2B5,2n%2B7
given:
%282n+%2B+1%29%282n+%2B+3%29+=+%282n+%2B+5%29%282n+%2B+7%29+-+64
4n%5E2+%2B+8n+%2B+3+=+4n%5E2+%2B+24n+%2B+35+-+64
8n+%2B+3+=+24n+-+29
16n+=+32
n+=+2
and
2n+%2B+1+=+5
2n+%2B+3+=+7
2n+%2B+5+=+9
2n+%2B+7+=+11
The numbers are 5,7,9, and 11
check:
5%2A7+=+9%2A11+-64
35+=+99+-+64
35+=+35
OK