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(8 - √32) and (8 + √32), which are approximately 2.343 and 13.657.

Let x be one number and y the other. So you have 2 equations with 2 unknowns:

(1) x * y = 32

(2) x + y = 16

Rearranging (2) for y to get y=16-x. Now substitute this expression into equation (1):

x * (16 - x) = 32

16x - x2 = 32

x2 - 16x + 32 = 0

Then solve the quadratic formula:

x = ( 16 ± √((-16)2 - 4 x 32) ) / 2

= ( 16 ± √(256 - 128) ) / 2

= ( 16 ± √128) / 2

= 8 ± √32

If we consider x = 8 + √32:

y = 16 - x = 16 - (8 + √32) = 16 - 8 - √32

y = 8 - √32

and vice-versa.

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