Question

The sum of squares of two consecutive even positive integers is $244$. Find the numbers.

Answer 1

Let the consecutive even integers be $2n$ and $2n+2$

$(2n{)}^2+(2n+2{)}^2=244$

$\Rightarrow 8n^2+8n+4=244$

$\Rightarrow n^2+n-30=0$

$\Rightarrow (n+6)(n-5)=0$

$\Rightarrow n=5$ ($n$ can’t be negative)

The numbers are $10$ and $12$.