The given info can be used to get other equations such as AB+AC+BC=1/2 AB^2+BA^2+AC^2+CA^2+CB^2+BC^2=2 etc
If you get a common denominator for the expression to be evaluated and expand like crazy you get a big algebra mess, but all of the pieces can be rearranged and refactored and end up as (8+1/2)/(-(40+3/4)) = -34/123