Answer:
The two consecutive even numbers are 12 and 14.
Step-by-step explanation:
Set up the equation, which turns out to be a quadratic, solve for n:
[tex](2n)^2+(2(n+1))^2=340\\4n^2+4n^2+8n+4=340\\8n^2+8n-336=0\\n^2+n-42=0\\\implies (n_1=-7),\,\,\,n_2=6[/tex]
We are looking for positive even numbers, so the solution -7 is not valid. The solution for n is 6, and the two consecutive even numbers are:
2*6=12
2*7=14
Test: 12*12 + 14*14 = 340
