The product of two positive consecutive integers is 11 more than their sum. Find the integers.
A) 3,4
B) $-5,-4$
C) 4,5
D) $-3,-2$

Question

Quizplus · Accepted Answer

The equation derived from the problem statement is $x(x + 1) = x + (x + 1) + 11$. Simplifying gives $x^2 + x = 2x + 12$, leading to $x^2 - x - 12 = 0$. Factoring gives $(x - 4)(x + 3) = 0$, so $x = 4$ or $x = -3$. Since we're looking for positive integers, $x = 4$, making the consecutive integers 4 and 5.

The Product of Two Positive Consecutive Integers Is 11 More −5,−4-5,-4−5,−4

The Product of Two Positive Consecutive Integers Is 11 More $-5,-4$