If $(x+k)(y+k)(z+k)=k$ for $k=1,2,3.$
Then value of $(x+4)(y+4)(z+4)$ is,
where $x,y,z$ are complex numbers.
what i try
$xyz+k^2(xy+yz+zx)+(x+y+z)k+k^3-k=0$
$\displaystyle \frac{k^2}{2}\bigg[(x+y+z)^2-(x^2+y^2+z^2)\bigg]+(x+y+z)k+xyz+k^3-k=0$
could some help me how do i solve it , thanks
Hint: $p(w) = (x+w)(y+w)(z+w) - w$ is a polynomial in $w$ of degree $3$ with the leading coefficient equal to one, and zeros at $w=1, 2, 3$.