\(1,\\ a,\Rightarrow x^2-x-x^2+2x+3=7\\ \Rightarrow x=4\\ b,\Rightarrow\left(x+1\right)^2=9\Rightarrow\left[{}\begin{matrix}x+1=3\\x+1=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-4\end{matrix}\right.\\ c,\Rightarrow x^2\left(x-5\right)+4\left(x-5\right)=0\\ \Rightarrow\left(x^2+4\right)\left(x-5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x^2=-4\left(vô.lí\right)\\x=5\end{matrix}\right.\Rightarrow x=5\\ 2,\\ a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)\\ =\left(-1\right)^3-3\left(-1\right)\left(-6\right)=-1-18=-19\)
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