let's call the first integer x, and the second y.
just to be able to talk about them.
one positive integer is 3 less than twice another
x = 2y -3
x² + y ² = 306
integers means whole numbers, and they must be positive.
x² + y ² = 306
can be rewritten as
x² = 306 -y²
x = sqrt(306 -y²)
sqrt means square root, obviously.
let's plug this last expression into
x² + y ² = 306
(sqrt(306 -y²))² = 2y -3
in this case, the square root and the (...)² cancel each other. so...
306 -y² = 2y -3
rewrite
309 -y² = 2y
309 = y² +2y
-----------------------------------
screw all this. I just tried it out with numbers in desmos (see screenshot), because I got stuck
the numbers are 9 and 15. it was honestly just easier to try inputs out than to solve this system.
sorry I can't give you insight here. but just doing it anyways might be the key massage.
