Question: Question on eliminate

1.

eliminate({-a+x+y+z, -b+x*y+y*z+x*z, -c+x*y*z, -P+x^4+y^4+z^4}, {x, y, z});
    [{x = (sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2+a*b*c-c^2)/(2*b*c),
      y = -(sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2-a*b*c+c^2)/(2*b*c),
      z = c/b}, {-a^4+4*a^2*b-4*a*c-2*b^2+P}],
    [{x = -(sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2-a*b*c+c^2)/(2*b*c),
      y = (sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2+a*b*c-c^2)/(2*b*c),
      z = c/b}, {-a^4+4*a^2*b-4*a*c-2*b^2+P}]

The expression for P is fine, but how are x and y square roots and z=c/b??

2.

eliminate({y*z, x+y-z}, z);
                       [{z = 0}, {x + y}]

Is this supposed to happen? I was expecting y*(x+y):

Groebner:-Basis({y*z, x+y-z}, lexdeg([z], [x, y]));
                     [x*y + y^2, z - x - y]