find 3 positive consecutive integers such that the product of the first and the third integer is 17 more than three times the second integer

Guest Apr 5, 2022

#2**+1 **

Let the 3 numbers be \(x, x+1, x+2\)

We have the equation:

\(x(x+2)=17+3(x+1)\)

Simplifying into a quadratic:

\(x^2 - x - 20 = 0\)

Factor:

\((x+4)(x-5) = 0\)

We want x to be positive, so x must equal 5, meaning the 3 integers are \(\color{brown}\boxed{5,6,7}\)

BuilderBoi Apr 5, 2022