a) Ta có: \(\left(2x-3\right)\left(3x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\3x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\3x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{4}{3}\end{matrix}\right.\)
Vậy: \(S=\left\{\dfrac{3}{2};-\dfrac{4}{3}\right\}\)
b) Ta có: \(x^3-3x^2+3x-1=\left(x-1\right)\left(x+1\right)\)
\(\Leftrightarrow\left(x-1\right)^3-\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2-2x+1-x-1\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-3x\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=3\end{matrix}\right.\)
Vậy: S={0;1;3}
c) Ta có: \(x^2+x=2x+2\)
\(\Leftrightarrow x\left(x+1\right)-2\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
Vậy: S={-1;2}
d) Ta có: \(\left(x-1\right)^2=2\left(x^2-1\right)\)
\(\Leftrightarrow\left(x-1\right)^2-2\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-1-2x-2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(-x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\-x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\-x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)Vậy: S={1;-3}
e) Ta có: \(2\left(x+2\right)^2-x^3-8=0\)
\(\Leftrightarrow2\left(x+2\right)^2-\left(x^3+8\right)=0\)
\(\Leftrightarrow2\left(x+2\right)\cdot\left(x+2\right)-\left(x+2\right)\left(x^2-2x+4\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(2x+4-x^2+2x-4\right)=0\)
\(\Leftrightarrow\left(x+2\right)\cdot\left(-x^2+4x\right)=0\)
\(\Leftrightarrow-x\left(x+2\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+2=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\\x=4\end{matrix}\right.\)
Vậy: S={0;-2;4}
