SOLUTION: I am thinking of three consecutive numbers. If I multiply the first with the second and then subtract three times the third the result is 57. What are the numbers?

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Question 158850: I am thinking of three consecutive numbers. If I multiply the first with the second and then subtract three times the third the result is 57. What are the numbers?
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
3 numbers:
a
a+1
a+2
words to symbols:
a(a+1)-3(a+2)=57
a^2+a-3a-6=57
a^2-2a-63=0
(a+7)(a-9)=0
so a=-7 or a=9. We want a to exist in the set of integers. Thus, we exclude a=-7 as a solution.
The numbers, then, are 9, 10, 11.
Check:
9(10)-3(11)=90-33=57
yes