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

Question 992703: The square of the sum of two consecutive positive even integers is greater than the sum of their squares by 48. Find two integer.
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
consecutive positive even integers: x, (x+2)

(x + (x+2))^2 = x^2 + (x+2)^2 + 48
(2x + 2)^2 = x^2 + (x+2)^2 + 48
4x^2 + 8x + 4 = x^2 + x^2 + 4x + 4 + 48
2x^2 + 4x - 48 = 0
x^2 + 2x - 24 = 0
(x + 6)(x - 4) = 0

The integers are positive, so x = 4. The integers are 4 and 6.
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