SOLUTION: find the consecutive integers whose product exceeds their sum by 41.

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Question 157454: find the consecutive integers whose product exceeds their sum by 41.
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let n, n+1 be the two consecutive numbers.
Their product can be expressed as n(n+1).
Their sum can be expressed as n+n+1.
As their product exceeds their sum by 41, we have
n(n+1)=n+n+1+41
Solve the equation for n, we have
n%5E2%2Bn=2n%2B42
n%5E2-n-42=0
%28n-7%29%28n%2B6%29=0
n = 7 or n = -6.
So the two consecutive numbers is
7,8
Or
-6,-5