I have a system of non-linear equations of the form

$A{x}_{1}^{B}\mathrm{exp}{\textstyle (}\frac{-C}{{x}_{1}}{\textstyle )}={k}_{1}$

$A{x}_{2}^{B}\mathrm{exp}{\textstyle (}\frac{-C}{{x}_{2}}{\textstyle )}={k}_{2}$

$A{x}_{3}^{B}\mathrm{exp}{\textstyle (}\frac{-C}{{x}_{3}}{\textstyle )}={k}_{3}$

where $[{x}_{1},{x}_{2},{x}_{3}]$ and $[{k}_{1},{k}_{2},{k}_{3}]$ are known. The couple of constants $[A,B,C]$ is the unknown. The solution of this non-linear system of equations is given here: Solving a system of non linear equations

We must now ensure that $B<0$ at all times. How would you find one couple $[{A}^{\prime},{B}^{\prime},{C}^{\prime}]$ that best approach the solution of the system, with ${B}^{\prime}<0$.