SOLUTION: given any three consecutive integers prove that the product of the first and third number is one less than the squareof the middle one

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Question 471539: given any three consecutive integers prove that the product of the first and third number is one less than the squareof the middle one
Answer by richard1234(7193) About Me  (Show Source):
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Let x, x+1, x+2 be the three integers. The product of the first and third number is x(x+2) = x^2 + 2x. The square of the middle one is (x+1)^2 = x^2 + 2x + 1. Hence the product of the first and third numbers is one less than the square of the middle one.