Question 54
Determine all triples of real numbers $(x, y, z)$, such that the equation
$$
4x^4 - x^2 (4y^4 + 4z^4 - 1) - 2xyz + y^8 + 2y^4z^4 + y^2z^2 + z^8 = 0
$$
holds.
$$
4x^4 - x^2 (4y^4 + 4z^4 - 1) - 2xyz + y^8 + 2y^4z^4 + y^2z^2 + z^8 = 0
$$
holds.