The sum of three consecutive integers is equal to their product. How many such possibilities are there?
Only one
Only two
Only three
No such possibility is there
Let the 3 consecutive integers be x - 1, x, and x + 1 According to the question, sum = product, therefore (x – 1) + x + (x + 1) = (x - 1) × x × (x + 1) ⇒ 3x = x × (x - 1) × (x + 1) ⇒ x = 0, 2 or -2 Therefore, there are 3 such possibilities. Hence, option (c) is the correct answer.
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