You said that (xy) = 16, and (x+y) = 4 .
From the second equation you can get [ x = 4 - y ],
then substitude that for 'x' in the first equation, and
finally, rearrange the first equation to read
x² - 4x + 16 = 0
Don't even try to factor that quadratic equation. Go straight
to the quadratic formula, and the two solutions you find are ...
x = 2 + i 2√3
and
x = 2 - i 2√3 .
Those are the two number that do what you want.
There are no real numbers that can do it.
