Question 10
Prove that the real-coefficient polynomial in $x, y, z$,
$$
x^{4}(x - y)(x - z) + y^{4}(y - z)(y - x) + z^{4}(z - x)(z - y),
$$
cannot be expressed as a finite sum of squares of real-coefficient polynomials in $x, y, z$.
$$
x^{4}(x - y)(x - z) + y^{4}(y - z)(y - x) + z^{4}(z - x)(z - y),
$$
cannot be expressed as a finite sum of squares of real-coefficient polynomials in $x, y, z$.