I am new here and I just want to ask if the following system has a general solution:

If $a$ $b$ and $c$ are given such that:

$$
x + y + z = a
$$

$$
x^2 + y^2 + z^2 = b
$$

$$
x^8 + y^8 + z^8 = c
$$

Is there a way to find out if there exists a general solution to find $x$, $y$ and $z$?