SOLUTION: Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number?

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Question 1045107: Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number?
Answer by ikleyn(52778) About Me  (Show Source):
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Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number?
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n%2A%28n%2B1%29 = %28n%2B2%29%5E2+-+19.


n%5E2+%2B+n = n%5E2+%2B+4n+%2B+4+-+19,

n = 4n - 15,

15 = 3n,

n = 5.

The three consecutive numbers are  5,  6,  and 7.