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Denote the lowest of the three consecutive numbers as n. Then the other numbers are n +1 and n +2. From the problem statement, n(n + 1) = (n + 2)2 -52, or:

n2 + n = n2 + 4n + 4 - 52, or 3n = 48, or n = 16. Check: 16 X 17 = 272; 18 X 18 = 324; 324 - 272 = 52.

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Q: Find 3 consecutive numbers where the product of the two smaller numbers is 52 less than the square of the larger number?
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