System of Complex Equations
Algebra
Level
3
\( x, y\) and \(z\) are complex numbers that satisfy the equations \(x+y+z = 2\), \(xy + yz + zx = 3\) and \(xyz =4\). Given that \( \frac {1}{1-x-yz} + \frac {1}{1-y-zx} + \frac {1}{1-z-xy} = \frac {a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is the value of \( a+b\)?
by
Calvin Lin