Answer:
5, 6, 7
Step-by-step explanation:
In order to solve for the three integers, we can assign a variable and set up an equation:
first integer: x
second integer: x + 1
third integer: x + 2
Given that 'the product of the first and third integer is 17 more than 3 times the second integer':
x(x + 2) = 3(x + 1) + 17
Distribute: x² + 2x = 3x + 3 + 17
Combine like terms: x² - x - 20 = 0
Factor: (x - 5)(x + 4) = 0
Set them equal to '0' and solve:
x - 5 = 0 x + 4 = 0
x = 5 x = -4
Since the problem asks for positive integers, x must equal 5:
first = 5
second = 5 + 1 = 6
third = 5 + 2 = 7
