Put a low resistance connecter between terminals A and B, shorting resistor z, and measure the conductance between that connector and C.
Call the answer z'.
z' is the sum of the conductances of resistors x and y.
Similarly measure conductances x' and y'.
Now the equations are:
x' = 1/y + 1/z
y' = 1/x + 1/z
z' = 1/x + 1/y
Add the first two equations and subtract the last and you get:
x' + y' − z' = 2/z ;
Whence z = 1/(2(x' + y' − z')).
Similarly x = 1/(2(z' + y' − x')) and y = 1/(2(x' + z' − y')).