SOLUTION: The sum of the squares of two consecutive even integers is 52. Find the integers.

Question 45329: The sum of the squares of two consecutive even integers is 52. Find the integers.
Answer by tutmath(14) (Show Source): You can put this solution on YOUR website!
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)

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