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For real numbers the geometric mean is always less than the arithmetic mean, so the answer must involve complex numbers.

x + y = 80

x * y = 3600

x * (80 - x) =3600

x^2 - 80x +3600 = 0

x = 0.5 * (80 +/- sqrt(80^2 - 4 * 3600)) = 40 +/- sqrt(40^2 - 3600)

= 40 +/- sqrt(2000) = 40 +/- 10 * sqrt(20)

so the two numbers must be imaginary and are:

10 * (4 + i * sqrt(20)) and

10 * (4 - i * sqrt(20))

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