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.

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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) About Me  (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.