A negative result on algebraic specifications of the meadow of rational numbers

$mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0$. In this note, we prove that $mathbb{Q}_0$ cannot be specified by the usual axioms for meadows augmented by a finite set of axioms of the form $(1+ cdots +1+x^2)cdot (1+ cdots +1 +x^2)^{-1}=1$.