Question

$$\left. \begin{array} { l } { 2 = a ^ { 2 } + 2 a b + b + b 2 } \\ { 882 } \end{array} \right.$$

Solve for a, b, b_2, c (complex solution)

$a=\sqrt{b^{2}-b-b_{2}+2}-b\text{, }b\in \mathrm{C}\text{, }b_{2}\in \mathrm{C}\text{, }c=882$
$a=-\sqrt{b^{2}-b-b_{2}+2}-b\text{, }b\in \mathrm{C}\text{, }b_{2}\in \mathrm{C}\text{, }c=882$

Solve for a, b, b_2, c

$\left\{\begin{matrix}\\a=\sqrt{b^{2}-b-b_{2}+2}-b\text{, }b\in (-\infty,\frac{-\sqrt{4b_{2}-7}+1}{2}]\cup [\frac{\sqrt{4b_{2}-7}+1}{2},\infty)\text{, }b_{2}\in \mathrm{R}\text{, }c=882\text{; }a=-\sqrt{b^{2}-b-b_{2}+2}-b\text{, }b\in (-\infty,\frac{-\sqrt{4b_{2}-7}+1}{2}]\cup [\frac{\sqrt{4b_{2}-7}+1}{2},\infty)\text{, }b_{2}\in \mathrm{R}\text{, }c=882\text{, }&\text{unconditionally}\\a=\sqrt{b^{2}-b-b_{2}+2}-b\text{, }b\in \mathrm{R}\text{, }b_{2}\in \mathrm{R}\text{, }c=882\text{; }a=-\sqrt{b^{2}-b-b_{2}+2}-b\text{, }b\in \mathrm{R}\text{, }b_{2}\in \mathrm{R}\text{, }c=882\text{, }&b_{2}\leq \frac{7}{4}\end{matrix}\right.$