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Find three positive consecutive integers such that the product of the smallest and the largest is 17 more than three times the median integer.

 Jan 12, 2020
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Since they are consecutive integers, they can be labeled:  a, a + 1, and a + 2

Product of the smallest and largest:  a(a + 2)

17 more than three times the median integer:  17 + 3(a + 1)

The equation:     a(a + 2)  =  17 + 3(a + 1)

                            a2 + 2a  =  17 + 3a + 3

                        a2 - a - 20  =  0

                    (a - 5)(a + 4)  =  0

                Either  a = 5  or  a = -4

Since they must be positive, we can only use  a = 5     --->   a + 1  =  6     --->     a + 2  =  7

 Jan 12, 2020

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