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 $z$?