Solve the problem.
-The sum of the squares of two consecutive integers is 365 . Find the integers.
A) 13,14
B) $- 13 , - 14$
C) 13,14 or $- 13 , - 14$
D) $13 , - 14$

Question

Quizplus · Accepted Answer

The equation for the sum of the squares of two consecutive integers, $n$ and $n+1$, is $n^2 + (n+1)^2 = 365$. Simplifying, we get $2n^2 + 2n - 364 = 0$, which simplifies further to $n^2 + n - 182 = 0$. Solving this quadratic equation, we find $n = 13$ or $n = -14$, which means the pairs are either $13, 14$ or $-14, -13$ (or $-13, -14$ when ordered as consecutive integers). Therefore, both $13, 14$ and $-13, -14$ are correct.

Solve the Problem −13,−14- 13 , - 14−13,−14 C) 13,14 Or −13,−14- 13 , - 14−13,−14

Solve the Problem $- 13 , - 14$ C) 13,14 Or $- 13 , - 14$