Let x and y be the two numbers. Then, we have:
x + y = 2 * 12 = 24
xy = 4 * 35 = 140
Solving for x and y, we use the first equation to substitute for y:
y = 24 - x
And then substitute that into the second equation:
x(24 - x) = 140
Expanding the right side:
24x - x^2 = 140
Rearranging:
x^2 - 24x + 140 = 0
Using the quadratic formula, we find:
x = (24 ± √(24^2 - 4 * 1 * 140)) / (2 * 1) = (24 ± √(576 - 560)) / 2
x = (24 ± √16) / 2 = (24 ± 4) / 2 = 26 / 2 = 13
So, x = 13 and y = 24 - x = 24 - 13 = 11.
The two numbers are 13 and 11