Question

The product of two consecutive positive integers is 19 more than their sum. Find the integers.

Answer 1

Two consecutive integers are "x" and "x+1"
Their sum is x + x + 1 = 2x + 1

So x(x+1) = 2x + 1 + 19 add like terms
x(x+1) = 2x + 20 distribute
x^2 + x = 2x + 20 set it = to 0
x^2 - x - 20 = 0 ... Now how do you solve these. Do you want me to factor or use the quadratic formula?

Answer 2

wouldnt it be (x-5)(x+4)?

Answer 3

Yes which then the answer are either 5 or -4 so the two integers are
5 and 6 5(6) = 5 + 6 + 19
and
-4 and -3 -4(-3) = -4 + -3 + 19