a) \(\left(x+\dfrac{1}{3}\right)\left(x-2\right)=0\)
\(\left(x+\dfrac{1}{3}\right)=0\)
\(\left(x-2\right)=0\)
\(\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=2\end{matrix}\right.\)
b)
\(4A.\\ a,\left(a+\dfrac{1}{3}\right)\left(x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{3}=0\\x-2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=2\end{matrix}\right.\\ b,\left(x^2+1\right)\left|2x-5\right|=0\\ \Rightarrow\left[{}\begin{matrix}x^2+1=0\\\left|2x-5\right|=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x^2=-1\left(vô.lí\right)\\2x-5=0\end{matrix}\right.\\ \Rightarrow x=\dfrac{5}{2}\)
\(c,x^2\left(2x-3\right)-9\left(2x-3\right)=0\\ \Rightarrow\left(x^2-9\right)\left(2x-3\right)=0\\ \Rightarrow\left(x-3\right)\left(x+3\right)\left(2x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-3=0\\x+3=0\\2x-3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-3\\x=\dfrac{3}{2}\end{matrix}\right.\)
\(d,2x^2-3x+1=0\\ \Rightarrow\left(2x^2-2x\right)-\left(x-1\right)=0\\ \Rightarrow2x\left(x-1\right)-\left(x-1\right)=0\\ \Rightarrow\left(2x-1\right)\left(x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}2x-1=0\\x-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\end{matrix}\right.\)
\(4B.\\ a,\left|3x-\dfrac{3}{4}\right|\left(-2-4x\right)=0\\ \Rightarrow\left[{}\begin{matrix}\left|3x-\dfrac{3}{4}\right|=0\\-2-4x=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}3x-\dfrac{3}{4}=0\\2x+1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}3x=\dfrac{3}{4}\\2x=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
\(b,4\left(-4+x\right)+x\left(x^2-16\right)=0\\ \Rightarrow b,4\left(x-4\right)+x\left(x-4\right)\left(x+4\right)=0\\ \Rightarrow4\left(x-4\right)+\left(x^2+4x\right)\left(x-4\right)=0\\ \Rightarrow\left(x-4\right)\left(x^2+4x+4\right)=0\\ \Rightarrow\left(x-4\right)\left(x+2\right)^2=0\\ \Rightarrow\left[{}\begin{matrix}x-4=0\\\left(x+2\right)^2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x+2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)
\(c,x^2+6x-7=0\\ \Rightarrow\left(x^2+7x\right)-\left(x+7\right)=0\\ \Rightarrow x\left(x+7\right)-\left(x+7\right)=0\\ \Rightarrow\left(x-1\right)\left(x+7\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-1=0\\x+7=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=-7\end{matrix}\right.\)
