The difference between two positive integers is 3. If the smaller is added to the square of the larger, the sum is 339. Find the integers.?

Set your variables. Let x equal the larger and y equal the lower.

The difference of the two is three. so x - y = 3

And x^2 + y =339

Solve the first equation for y and insert into the second. y = x - 3

So x^2 + x - 3 = 339

Subtract 339 from both sides. x^2 + x - 342 = 0

Factor out (x+19)(x-18) = 0

Thus x is 18 and -19 but the question ask for two positive values so drop the negative one and use the first equation to solve for y

x = 18, y = 15

x+(x+3)^2 = 339
x^2+7x-330 =0
(x+22)(x-15) = 0
x = 15
Numbers are 15 and 18

y = x + 3
y^2 + x = 339

(x+3)^2 + x = 339
x^2 + 7x - 330 = 0
x = 15, -22

x = 15, y = 18

quadratic equation:
given that n-k=3
n+ k^2 =339
so 3+k=339-k^2
k^2+k-333=0
k=-1/2 +/- sqrt(1333)/2
take the positive number