SOLUTION: The product of two consecutive integers is 16 less than the square of the next larger integer. What are the three integers?

Question 921999: The product of two consecutive integers is 16 less than the square of the next larger integer. What are the three integers?
Answer by multiplier(8) (Show Source): You can put this solution on YOUR website!

say n= smallest number
(n+1)= middle number
(n+2)= largest number
1 is added to the next number because these 3 numbers are consecutive
the product of two consecutive integers is 16 less than the square of the next larger:
n(n+1)= {(n+2)^2}-16 or {n(n+1)}+16= (n+2)^2
simplifying:
n=4 smallest number
(n+1)=5 next number
(n+2)=6 largest number

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