What is the smallest possible value for the product of 2 integers that differ by 7

Let 2 integers that differ by 7 are x , x+7

let the product of the 2 integers that differ by 7 is y


∴ y = x(x+7) = x² + 7x


By graphing y = x² + 7x ⇒⇒⇒ see the attached figure

There is a minimum point at x = -3.5  which give y = -12.25
∵ The product of two integers will be an integer number
So, the nearest integer number to the minimum value = -12

∴ The smallest possible value for the product of 2 integers that differ by 7 is (-12)

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