Posted by **Nelson** on Monday, December 7, 2009 at 3:07pm.

Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.

- Algebra -
**Reiny**, Monday, December 7, 2009 at 3:15pm
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

(x-7)(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

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