Solve the problem.
-The product of two consecutive integers is 41 more than their sum. Find the integers.
A) 7, 8
B) -6, -5
C) 7, 8 or -6, -5
D) 6, 7 or -6, -5

Question

Quizplus · Accepted Answer

Let the two consecutive integers be $x$ and $x+1$. Their product is $x(x+1)$ and their sum is $x + (x+1) = 2x + 1$. The equation based on the given information is $x(x+1) = 2x + 1 + 41$, simplifying to $x^2 + x = 2x + 42$, and further to $x^2 - x - 42 = 0$. Factoring the quadratic equation gives $(x-7)(x+6) = 0$, leading to $x = 7$ or $x = -6$, thus the consecutive integers are either 7 and 8 or -6 and -5.

Solve the Problem. -The Product of Two Consecutive Integers Is 41 More Than