\(x^2-1+2x\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)+2x\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1+2x\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\3x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\3x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-1}{3}\end{matrix}\right.\)
\(\text{Vậy phương trình có tập nghiệm là }S=\left\{1;\dfrac{-1}{3}\right\}\)
\(x^2-1+2x\left(x-1\right)=0\)
\(\Leftrightarrow x^2-1+2x^2-2x=0\)
\(\Leftrightarrow\left(x^2+2x^2\right)-2x=1\)
\(\Leftrightarrow3x^2-2x-1=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)
\(x^2-1+2x\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-1\right)+2x\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x+1+2x\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x+1\right)=0\)
\(\Leftrightarrow x-1=0hoặc3x+1=0\)
\(\Leftrightarrow x=1hoặcx=\dfrac{-1}{3}\)
