I am new here and I just want to ask if the following system has a general solution:
$$
If a, b and c are given such that:
$$
$$
x + y + z = a
$$
$$
x² + y² + z² = b
$$
$$
xⁿ + yⁿ + zⁿ = c
$$
$$
Where n = 8.
$$
$$
Is there a way to find out if there exists a general solution to find x, y and z?