Let z be those complex numbers which satisfy |z+5| ≤ 4 and z(1+i)+z̄(1-i) ≥-10, i=√ -1. If the maximum value of |z+1|^2 is α+β √ 2, then the value of…

Let $\displaystyle z$ be those complex numbers which satisfy $$|z+5| \leq 4 \text { and } z(1+i)+\bar{z}(1-i) \geqslant-10, i=\sqrt{-1} . $$ If the maximum value of $\displaystyle |z+1|^2$ is $\displaystyle \alpha+\beta \sqrt{2}$, then the value of $\displaystyle (\alpha+\beta)$ is \_\_\_\_.