$\displaystyle \begin{array}{{>{\displaystyle}l}} Ta\ có:\ a^{2} +b^{2} =( a+b)^{2} -2ab=2^{2} -2( -1) =6\\ a^{3} +b^{3} =( a+b)^{3} -3ab( a+b) =2^{3} -3.( -1) .2=14\\ a^{5} +b^{5} =\left( a^{3} +b^{3}\right)\left( a^{2} +b^{2}\right) -a^{2} b^{2}( a+b) =14.6-2=82\\ |a+b|=\sqrt{( a+b)^{2} -4ab} =\sqrt{2^{2} +4} =2\sqrt{2}\\ a^{7} +b^{7} =\left( a^{4} +b^{4}\right)\left( a^{3} +b^{3}\right) -a^{3} b^{3}( a+b)\\ =\left[\left(( a+b)^{2} -2ab\right)^{2} -2a^{2} b^{2}\right]( a+b)\left[( a+b)^{2} -3ab\right]\\ =\left( 2^{2} -2\right) .2.\left( 2^{2} +3\right) =28 \end{array}$
