Answer:
the two positive integers are x= 15, and y = 11
Step-by-step explanation:
Let the first integer be x
Let the second integer be y
from the problem we can decode the following equations
---------------------------- equation 1
-------------------------equation 2
substituting the value of x into equation 2, we have
![(2y-7)^{2} + y^{2}= 346 --------------equation 3](https://tex.z-dn.net/?f=%282y-7%29%5E%7B2%7D%20%2B%20y%5E%7B2%7D%3D%20346%20--------------equation%203)
expanding, we have
![4y^{2}-28y+49+y^{2}=346](https://tex.z-dn.net/?f=4y%5E%7B2%7D-28y%2B49%2By%5E%7B2%7D%3D346)
![5y^{2}-28y-297 = 0](https://tex.z-dn.net/?f=5y%5E%7B2%7D-28y-297%20%3D%200)
from this, y = 11 or y = -5.4
since our answer is a positive integer, we will have to pick the first value of y which is y = 11
substituting the value of y into equation 1, we have
![x= 2(11)-7=15](https://tex.z-dn.net/?f=x%3D%202%2811%29-7%3D15)
hence x = 15
Therefore, we have x= 15, and y = 11
these are the two positive integers