3)
\(x^3-7x+6=0\)
\(\Leftrightarrow x^3+3x^2-3x^2-9x+2x+6=0\)
\(\Leftrightarrow\left(x^3+3x^2\right)-\left(3x^2+9x\right)+\left(2x+6\right)=0\)
\(\Leftrightarrow x^2\left(x+3\right)-3x\left(x+3\right)+2\left(x+3\right)=0\)
\(\Leftrightarrow\left(x^2-3x+2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-3\end{matrix}\right.\)
4) \(\left(2x+1\right)^2=\left(x-1\right)^2\)
\(\Leftrightarrow\left(2x+1\right)^2-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(2x+1-x+1\right)\left(2x+1+x-1\right)=0\)
\(\Leftrightarrow3x\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
Vậy ................
2.
\(2x^3+5x^2-3x=0\)
\(\Leftrightarrow2x^3+6x^2-x^2-3x=0\)
\(\Leftrightarrow\left(2x^3+6x^2\right)-\left(x^2+3x\right)=0\)
\(\Leftrightarrow2x^2\left(x+3\right)-x\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(2x^2-x\right)=0\)
\(\Leftrightarrow x\left(x+3\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+3=0\\2x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=\dfrac{1}{2}\end{matrix}\right.\)
