The 3 positive consecutive integers are 5, 6 and 7
Let the consecutive positive integers be x - 1, x and x + 1
If the product of the first and the third integer is 17 more than three times the second integer, this is expressed as:
(x-1)(x +1) = 3x + 17
Expand the expression:
x² - 1 = 3x + 17
x² - 3x = 17 + 1
x² - 3x - 18 = 0
Factorize the result
x² - 6x + 3x - 18 = 0
x(x-6) + 3(x - 6) = 0
(x - 6) (x+ 3) = 0
x = 6 and -3
if x = 6
First integer = x - 1 = 6 - 1 = 5
Second integer = 6
Third integer = x + 1 = 6 + 1 = 7
Hence the 3 positive consecutive integers are 5, 6 and 7
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