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
+2666 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 \(\color{brown}\boxed{5,6,7}\)
