SOLUTION: The product of two consecutive integers is 71 more than their sum. Find the integers.

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Question 1171785: The product of two consecutive integers is 71 more than their sum. Find the integers.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

    xy = x + y + 71.


It implies


    xy - x - y + 1 = 72


    (x-1)*(y-1) = 72.


It has two basic solutions


         a)  x-1 = 8,  y-1 = 9,   which implies  x= 9, y= 10

    and

         b)  x-1 = -8,  y-1 = -9, which implies x= -7,  y= -8.



ANSWER.  There are two pairs of such integer numbers.

         One pair is  (9,10).  The other pair is (-8,-7).



CHECK.   9*10 - 9 - 10 = 90 - 19 = 71.    ! Correct !

         (-8)*(-7) - (-8) - (-7) = 56 + 8 + 7  = 71.    ! Correct !

Solved.

I hope I impressed you by my solution (!)