Løs e^2k+lambda+|2k+lambda-1|+e^k-lambda-1+|kappa-lambda-2|=4

$$e ^ { 2 k + \lambda } + | 2 k + \lambda - 1 | + e ^ { k - \lambda - 1 } + | \kappa - \lambda - 2 | = 4$$

Løs for κ

$$\left\{\begin{matrix}\kappa =7-e^{k-\lambda -1}-e^{\lambda +2k}-2k\text{, }&5-e^{k-\lambda -1}-e^{\lambda +2k}-\lambda -2k\geq 0\text{ and }k\geq \frac{1-\lambda }{2}\\\kappa =2k+2\lambda +e^{\lambda +2k}+e^{k-\lambda -1}-3\text{, }&k\geq \frac{1-\lambda }{2}\text{ and }2k+\lambda +e^{\lambda +2k}+e^{k-\lambda -1}-5\leq 0\\\kappa =2k+2\lambda -e^{\lambda +2k}-e^{k-\lambda -1}+5\text{, }&2k+\lambda -e^{\lambda +2k}-e^{k-\lambda -1}+3\geq 0\text{ and }k\leq \frac{1-\lambda }{2}\\\kappa =-2k+e^{\lambda +2k}+e^{k-\lambda -1}-1\text{, }&-2k-\lambda +e^{\lambda +2k}+e^{k-\lambda -1}-3\leq 0\text{ and }k\leq \frac{1-\lambda }{2}\end{matrix}\right,$$