Solve the problem.
-Find three consecutive odd integers such that the sum of all three is 36 less than the product of the smaller two.
A) 7, 9, 11
B) 7, 9, 11, or -6, -4, -2
C) 5, 7, 9
D) -6, -4, -2

Question

Quizplus · Accepted Answer

Let the three consecutive odd integers be $x$, $x+2$, and $x+4$. The sum of these integers is $x + (x+2) + (x+4) = 3x + 6$. The product of the smaller two is $x(x+2)$. According to the problem, $3x + 6 = x(x+2) - 36$. Simplifying, we get $3x + 6 = x^2 + 2x - 36$, which simplifies further to $x^2 - x - 42 = 0$. Factoring, we find $(x-7)(x+6) = 0$, so $x = 7$ or $x = -6$. Thus, the sets of integers are $7, 9, 11$ or $-6, -4, -2$. However, since the question asks for odd integers, the correct answer is $7, 9, 11$.

Solve the Problem. -Find Three Consecutive Odd Integers Such That the Sum of the Sum