Algebra
posted by Nelson on .
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.

let the two numbers be x and x+1
then x(x+1) = x + y + 41
expanding and simplifying we get
x^2  x  42 = 0
(x7)(x+6) = 0
x = 7 or x = 6
case 1: the two numbers are 7 and 8
check: product = 56
sum = 15, 56 is greater than 15 by 41
case 2: the two numbers are 6 and 5
check: product is 30
sum is 11
30 is 41 greater than 11
so the two numbers are either 7 and 8 or
6 and 5