Solve the problem.
-Find three consecutive integers such that the square of the sum of the smaller two is 72 more than the square of the largest.
A) -5, -4, -3
B) 5, 6, 7, or -5, -4, -3
C) 5, 6, 7
D) 3, 5, 7

Question

Quizplus · Accepted Answer

Let the three consecutive integers be $x$, $x+1$, and $x+2$. The problem states that $(x + (x+1))^2 = (x+2)^2 + 72$. Simplifying gives $4x^2 + 4x + 1 = x^2 + 4x + 4 + 72$, which simplifies to $3x^2 - 75 = 0$. Solving this quadratic equation gives $x = 5$ or $x = -5$, leading to the sets of integers $5, 6, 7$ and $-5, -4, -3$.

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