Kaplansky's conjecture for the three remaining ternary forms

Let $x,y,z$ range over the integers, and consider the following three positive-definite ternary quadratic forms:

$$x^{2}+2y^{2}+5z^{2}+xz,$$ $$x^{2}+3y^{2}+6z^{2}+xy+2yz,$$

and

$$x^{2}+3y^{2}+7z^{2}+xy+xz.$$

Kaplansky's conjecture. Each of these ternary quadratic forms represents every positive odd integer; that is, for every positive odd integer $n$, the equation $Q(x,y,z)=n$ is solvable in integers $x,y,z$ for each of the three displayed forms $Q$. These are the three remaining candidates from Kaplansky's classification of ternary forms representing all positive odd integers. The supplied context says that they had yet to be treated, so the conjecture is recorded as open here.