Solve the problem.
-Find three consecutive integers such that the sum of the squares of the smaller two is equal to the square of the largest.
A) -1, 0, 1
B) 3, 4, 5
C) -1, 0, 1 or 3, 4, 5
D) -3, -4, -5

Question

Quizplus · Accepted Answer

The problem can be solved algebraically by letting the three consecutive integers be $x$, $x+1$, and $x+2$. The equation based on the given condition is $x^2 + (x+1)^2 = (x+2)^2$. Solving this equation, we find that it holds true for $x = -1$ and $x = 3$, which correspond to the sets of integers $-1, 0, 1$ and $3, 4, 5$ respectively. Therefore, both sets of integers satisfy the condition.

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