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
[tex]x=2y-7[/tex] ---------------------------- equation 1
[tex]x^{2} + y^{2}= 346[/tex] -------------------------equation 2
substituting the value of x into equation 2, we have
[tex](2y-7)^{2} + y^{2}= 346 --------------equation 3[/tex]
expanding, we have
[tex]4y^{2}-28y+49+y^{2}=346[/tex]
[tex]5y^{2}-28y-297 = 0[/tex]
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
[tex]x= 2(11)-7=15[/tex]
hence x = 15
Therefore, we have x= 15, and y = 11
these are the two positive integers
