SOLUTION: Find 4 consecutive even integers where the product of two smaller numbers is 56 less than the product of the two larger numbers.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find 4 consecutive even integers where the product of two smaller numbers is 56 less than the product of the two larger numbers.      Log On


   

Question 178836: Find 4 consecutive even integers where the product of two smaller numbers is 56 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!
Call the smallest interger n
The next larger even integer is n+%2B+2
The next larger even integer is n+%2B+4
The next larger even integer is n+%2B+6
given:
n%28n%2B2%29+=+%28n%2B4%29%28n%2B6%29+-+56
n%5E2+%2B+2n+=+n%5E2+%2B+10n+%2B+24+-+56
8n+=+56+-+24
8n+=+32
n+=+4
n%2B2+=+6
n%2B4+=+8
n%2B6+=+10
The numbers are 4,6,8,and 10
check:
n%28n%2B2%29+=+%28n%2B4%29%28n%2B6%29+-+56
4%284%2B2%29+=+%284%2B4%29%284%2B6%29+-+56
4%2A6+=+8%2A10+-+56
24+=+24
OK