To find sin(x) * cos(x), we need to first solve the equation sin(x) + cos(x) = 1/3.

Given sin(x) + cos(x) = 1/3, we can square both sides of the equation to get rid of the square root:

(sin(x) + cos(x))^2 = (1/3)^2
sin^2(x) + 2sin(x)cos(x) + cos^2(x) = 1/9

Now, we know that sin^2(x) + cos^2(x) = 1, so we can substitute this in:

1 + 2sin(x)cos(x) = 1/9
2sin(x)cos(x) = 1/9 - 1
2sin(x)cos(x) = -8/9

Divide by 2 to solve for sin(x) * cos(x):

sin(x)cos(x) = -8/18
sin(x)cos(x) = -4/9

Therefore, sin(x) * cos(x) = -4/9.