28 The minimum value of the function $y=\sqrt{x^{2}+9}+\sqrt{x^{2}-8 x+17}$ is
$284 \sqrt{2}$. Since $\sqrt{a_{1}^{2}+b_{1}^{2}}+\sqrt{a_{2}^{2}+b_{2}^{2}} \geqslant \sqrt{\left(a_{1}+a_{2}\right)^{2}+\left(b_{1}+b_{2}\right)^{2}}$, thus $\sqrt{x^{2}+9}+$ $\sqrt{(x-4)^{2}+1} \geqslant \sqrt{4^{2}+(3+1)^{2}}=4 \sqrt{2}$. Equality holds when $\frac{x}{4-x}=\frac{3}{1}$, i.e., $x=3$.