Question 21301
I didn't get your answer, but it appears it is not solvable.
Let X = 1st even integer
X+2 = next even integer
X=4 = 3rd even integer
4(X+4)^2 -3X^2 - 41 = 2(X+2)^2
4(X^2 + 8X + 16) - 3X^2 - 41 = 2(X^2 + 4X + 4)
4X^2 + 32X + 64  - 3X^2 - 41 = 2X^2  + 8X + 8
X^2 - 24X - 15 = 0

doesn't yield even integers