$\text{Đáp án + Giải thích các bước giải:}$
`|a-b|+(2a+b+6)^{2}=0`
`\text{Vì}` $\left\{\begin{matrix}|a-b|≥0& \\(2a+b+6)^{2}≥0& \end{matrix}\right.$
`=>|a-b|+(2a+b+6)^{2}≥0`
`\text{Mà theo đề bài :}` `|a-b|+(2a+b+6)^{2}=0`
`=>` $\left\{\begin{matrix}|a-b|=0& \\(2a+b+6)^{2}=0& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}a-b=0& \\2a+b+6=0& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}a=b& \\2a+b=-6& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}a=b& \\2b+b=-6& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}a=b& \\3b=-6& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}a=-2& \\b=-2& \end{matrix}\right.$
`\text{Vậy}` `a=b=-2`
