$\displaystyle \begin{array}{{>{\displaystyle}l}} A=\sqrt{20a+92+\sqrt{a^{4} +16a^{2} +64}} ;B=a^{4} +20a^{3} +102a^{2} +40a+200\\ a) \ A=\sqrt{20a+92+\sqrt{\left( a^{2} +8\right)^{2}}}\\ A=\sqrt{20a+92+a^{2} +8\ }\\ A=\sqrt{a^{2} +20a+100}\\ A=\sqrt{( a+10)^{2}} =a+10\ \\ b) \ A+B=0\ \\ \rightarrow a^{4} +20a^{3} +102a^{2} +41a+210=0\ \\ \rightarrow a^{4} +10a^{3} +10a^{3} +100a^{2} +2a^{2} +20a+21a+210=0\ \\ \rightarrow a^{3}( a+10) +10a^{2}( a+10) +2a( a+10) +21( a+10) =0\\ \rightarrow ( a+10)\left( a^{3} +10a^{2} +2a +21\right) =0\\ \rightarrow a=-10\ \\ ( còn\ nghiệm\ bên\ kia\ xấu\ qyá\ mình\ vẫn\ chưa\ nghĩ\ ra\ cách\ tách\ ) \end{array}$
