Answer:
12, 14 are two consecutive positive even numbers
Step-by-step explanation:
Let x, x+2 are two consecutive positive even numbers
According to given Condition
![x^{2} + (x+2)^{2} = 340](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20%28x%2B2%29%5E%7B2%7D%20%3D%20340)
![x^{2} +x^{2} + 4 + 4x = 340](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2Bx%5E%7B2%7D%20%20%2B%204%20%2B%204x%20%3D%20340)
![2x^{2} + 4 + 4x - 340 = 0](https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%20%2B%204%20%2B%204x%20-%20340%20%3D%200)
![2x^{2} + 4x - 336 = 0](https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B%204x%20-%20336%20%3D%200)
![2x^{2} +28x -24x - 336 = 0](https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B28x%20-24x%20-%20336%20%3D%200)
![(2x^{2} +28x) -(24x + 336) = 0](https://tex.z-dn.net/?f=%282x%5E%7B2%7D%20%2B28x%29%20-%2824x%20%2B%20336%29%20%3D%200)
![2x(x} +14) - 24(x + 14) = 0](https://tex.z-dn.net/?f=2x%28x%7D%20%2B14%29%20-%2024%28x%20%2B%2014%29%20%3D%200)
![(2x -24) (x + 14) = 0](https://tex.z-dn.net/?f=%282x%20-24%29%20%28x%20%2B%2014%29%20%3D%200)
or ![x+14 = 0](https://tex.z-dn.net/?f=x%2B14%20%3D%200)
or ![x = -14](https://tex.z-dn.net/?f=x%20%3D%20-14)
As Number is positive so x = 12
x+ 2= 14
12, 14 are two consecutive positive even numbers
21 and 22 are two consecutive numbers whose squares, when subtracted, equals 43.