Question

Find two consecutive even natural numbers, such that the sum of their squares is $340$.

Answer 1

Let the even numbers be $n,n+2$

Given that $n^2+{(n+2)}^2=340$

$n^2+n^2+4+4n=340$

$2n^2+4n-336=0$

$n^2+2n-168=0$

$n^2+14n-12n-168=0$

$n(n+14)-12(n+14)=0$

$n=12,-14$

$\therefore n=12$

$\therefore$ numbers are $12$ and $14$