Question 45329
Let the first even integer be denoted by x
Then the next consecutive even integer will be (x + 2)

The problem states that the sum of their squares is 52

x^2 + (x + 2)^2 = 52

x^2 + x^2 + 4x + 4 = 52

2x^2 + 4x - 48 = 0

(You can also solve using the quadratic formula or by the method below)

2x^2 + 12x - 8x - 48 = 0 

2x(x + 6) - 8 (x + 6) = 0

(2x - 8)(x + 6) = 0

x = 8/2 = 4 or x = -6

If x = 4, then the next consecutive even integer is x + 2 = 6

If x = -6, then the next consecutive even integer is x + 2 = -4

If the integers are positive, the solution is only 4 and 6.
Otherwise, -4 and -6 is also a possible solution.


(If you have any questions regarding the solution you can ask me at tutmath@gmail.com)