Question

The sum of the squares of two consecutive positive even integers is 340. Write an equation and find the integers.

Answer 1

\[(2n)^2+(2n+2)^2=340\]

Answer 2

\[8n^2+8n+4=340\]
\[8n^2+8n-366=0\]
\[n^2+n-45=0\]
\[(n-6)(n+7)=0\]
\[n=6\] or \[n=-7\]
choose n = 6