Each of A, B and C is a complex number such that:

A+B+C = 2, and:
A² + B² + C² = 3, and:
A*B*C = 4

Evaluate:
(A*B + C - 1)^-1 + (B*C + A - 1)^-1 + (C*A + B - 1)^-1

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

Which is the solution assuming I made no errors. 

Posted by Jer on 2015-11-08 11:26:25