If the system of equation ${\mathrm{r}}^2+{\mathrm{s}}^2=\mathrm{t}$ and $\mathrm{r}+\mathrm{s}+\mathrm{t}=\frac{\mathrm{k}-3}{2}$ has exactly one real solution, then the value of $\mathrm{k}$ is

The equation $x^2+bx+c=0$ has distinct roots. If $2$ is subtracted from each root, the result are the reciprocal of the original roots, then $b^2+c^2$ is

Let $a, b, c$ and $m\in R^{+},$ the possible value of $m$ (independent of $a, b$ and $c$) for which at least one of the following equations have real roots, is

$a{x}^2+bx+cm=0$, $b{x}^2+cx+am=0$, $c{x}^2+ax+bm=0$.