One positive integer is 3 less than twice another. th sum of their squares is 306. find the integers ​

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

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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.

b is the final answer! : )