if two of x,y,z equals, we can easily get x=y=z. so x,y ,z difers from each other. from the original equations, we got quadratic equation $(k^2-1)x^2-k(k^2-1)x+(k^2-1)=0$, it has three different roots. so $k^2-1=0$ , k=1 , -1

$k=-xyz$ the rest is easy

India 1997