SOLUTION: Write down an equation representing the fact that the product of two consecutive integers is 15 greater than the greater of the two integers. Solve your equation to find all the pa

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Question 996209: Write down an equation representing the fact that the product of two consecutive integers is 15 greater than the greater of the two integers. Solve your equation to find all the pairs of integers for which the above description is true.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Write down an equation representing the fact that the product of two consecutive integers is 15 greater than the greater of the two integers.
Solve your equation to find all the pairs of integers for which the above description is true.
:
Two integers: n, n-1
:
n(n-1) = n + 15
n^2 - n - n - 15 = 0
n^2 - 2n -15 = 0
Factors to
(n-5)(n+3) = 0
Two solutions
n = 5 and 4
n = -3 an -4
;
:
Check the 1st solution: 5 * 4 = 5 + 15
Check the 2nd solution: -3*-4 = -3 + 15