SOLUTION: Find three consecutive natural numbers such that the square of the smallest number is 65 less than the product of the remaining two numbers.

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Question 1061060: Find three consecutive natural numbers such that the square of the smallest number is 65 less than the product of the remaining two numbers.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the three numbers be N-1, N, and N+1.
%28N-1%29%5E2=N%28N%2B1%29-65
N%5E2-2N%2B1=N%5E2%2BN-65
-3N=-66
N=22
So the numbers are 21,22, and 23.
Verifying,
21%5E2=22%2A23-65
441=506-65
441=441
True, good solution.