How do you find two consecutive even integers that have 452 as the sum of their squares?

Nov 13, 2016

$- 16 , 14$

Explanation:

Two consecutive even integers can be represented as

$2 n , 2 n + 2$ so the condition is

${\left(2 n\right)}^{2} + {\left(2 n + 2\right)}^{2} = 452$. Solving for $n$ we have

$n = - 8$ and $n = 7$ so the numbers are

$- 16$ and $14$