\(a,\left(x-1\right)\left(x^2+3x-2\right)-\left(x^3-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^2+3x-2\right)-\left(x-1\right)\left(x^2+x+1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^2+3x-2-x^2-x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(2x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\2x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{3}{2}\end{matrix}\right.\)
C1 : \(b,\left(x^3+x^2\right)+\left(x^2+x\right)=0\)
\(\Rightarrow x^2\left(x+1\right)+x\left(x+1\right)=0\)
\(\Rightarrow x\left(x+1\right)\left(x+1\right)=0\)
\(\Rightarrow x\left(x+1\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
C2 : \(b,\left(x^3+x^2\right)+\left(x^2+x\right)=0\)
\(\Rightarrow x^3+x^2+x^2+x=0\)
\(\Rightarrow x^3+2x^2+x=0\)
\(\Rightarrow x\left(x^2+2x+1\right)=0\)
\(\Rightarrow x\left(x+1\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left(x+1\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
a) \(\left(x-1\right)\left(x^2+3x-2\right)-\left(x^3-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+3x+2\right)-\left(x-1\right)\left(x^2+x+1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{2}\end{matrix}\right.\)
Vậy phương trình có tập nghiệm \(S=\left\{1;-\dfrac{1}{2}\right\}\)
b) \(\left(x^3+x^2\right)+\left(x^2+x\right)=0\)
\(\Leftrightarrow x^2\left(x+1\right)+x\left(x+1\right)=0\)
\(\Leftrightarrow\left(x^2+1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x^2+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x^2=-1\left(loại\right)\end{matrix}\right.\)
Vậy phương trình có tập nghiệm\(S=\left\{-1\right\}\)
