the square of the sum of two consecutive positive even integer is greater than the sum of their square by 48. Find two integers.

Answer 1

x and x+2

x^2 + (x+2)^2 = (2x+2)^2 - 48

x^2 + x^2 + 4 x + 4 = 4 x^2 + 8 x + 4 - 48

2 x^2 + 4 x - 48 = 0

x^2 + 2 x - 24 = 0

(x -4)(x+6) = 0
x = 4 and x+2 = 6