Determine two consecutive even positive integers,  the sum of whosesquares is 100.

Let the two consecutive odd natural numbers be x and x + 2.
x ² + (x + 2) ² = 100
x ² + x ² + 4x + 4 = 100
2x ² + 4x – 96 = 0
x ² + 2x – 48 = 0
x ² + 8x – 6x – 48 = 0
x(x + 8) – 6(x + 8) = 0
(x – 6)(x + 8) = 0
(x – 6) = 0 or (x + 8) = 0
x = 6 or x = – 8
The two consecutive even positive integers is 6 and 8.
Checking:
6 ² + 8 ² = 36 + 64 = 100.