Question

The product of two consecutive integers is 71 more than their sum. Find the integers.

Answer 1

\[n(n+1)=n+n+1+71\] is a start

Answer 2

(x)(x+1) = 71 + (x + x+ 1)
x^2 + x = 71 + 2x + 1
x^2 - x -72 = 0
(x-9)(x+8) = 0
x = 9; x = -8

if x =9, x+1 = 10
if x = -8, x = -7