Answer:
13 and 389
Step-by-step explanation:
Let the two positive integers be x and y
If a positive integer is 38 more than 27 times another, then;
x = 27y+ 38 ...1
If their product is 5057, then;
xy = 5057 .....2
Substitute equation 1 into 2
(27y + 38)y = 5057
Expand the bracket
27y^2 + 38y = 5057
27y^2 + 38y - 5057 = 0
Factorize
27y^2 -351y + 389y - 5057 = 0
27y(y-13) + 389(y-13) =0
(27y+389)(y−13) = 0
27y + 389 = 0 and y - 13 = 0
27y = -389 and y = 13
Since y is a positive integer, hence y = 13
Substiute y = 13 into equation 1;
x = 27y+ 38 ...1
x = 27(13)+ 38
x = 351 + 38
x= 389
Hencethe two positive integers are 13 and 389