SOLUTION: The product of two consecutive integers is 36 less than six times their sum. Find the integers. Given the answers as comma-separated numbers in ascending order. I only can find o

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Question 1140662: The product of two consecutive integers is 36 less than six times their sum. Find the integers. Given the answers as comma-separated numbers in ascending order.
I only can find one set of numbers every time never two. If I do find the two, I do find the two and I'm off by a negative or I did the next number down besides up.
PLEASE PLEASE HELP!!!
Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.
n*(n+1) = 6*(n+(n+1)) - 36


n^2 + n = 12n + 6 - 36


n^2 - 11n + 30 = 0


(n-5)*(n-6) = 0


There are two roots:  n= 5  and  n= 6.


CHECK for n= 5:  5*(5+1) = 5*6 = 30;   6*(5+6) - 36 = 6*11 - 36 = 66 - 36 = 30, the same number.   ! Correct !



CHECK for n= 6:  6*(6+1) = 6*7 = 42;   6*(6+7) - 36 = 6*13 - 36 = 78 - 36 = 42, the same number.   ! Correct !


ANSWER.  The problem has TWO PAIRS of consecutive integer solutions:  (5,6)  and  (6,7).

Solved.


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