Question 12Which of the following conditions is sufficient to guarantee that integers $x,$ $y,$ and $z$ satisfy the equation $$ x(x-y)+y(y-z)+z(z-x) $$$$ = 1? $$$ x > y$ and $y=z$$ x=y-1$ and $y=z-1$$ x=z+1$ and $y=x+1$$ x=z$ and $y-1=x$$ x+y+z=1 $