A gas has the equation of state [frac{p v_{m}}{Re T}=1+mathrm{A} pleft(T^{3}-9.75 T_{mathrm{c}} T^{2}+9 T_{mathrm{c}}^{2} T ight)+mathrm{B} p^{2}

A gas has the equation of state

\[\frac{p v_{m}}{\Re T}=1+\mathrm{A} p\left(T^{3}-9.75 T_{\mathrm{c}} T^{2}+9 T_{\mathrm{c}}^{2} T\right)+\mathrm{B} p^{2} T\]

where \(\mathrm{A}\) and \(\mathrm{B}\) are positive constants and \(T_{\mathrm{c}}\) is the critical temperature. Determine the maximum and minimum inversion temperatures, expressed as a multiple of \(T_{\mathrm{c}}\). \(\left[6 T_{c} ; 0.5 T_{\mathrm{c}}\right]\)