a/\(x\left(x-2\right)=x\left(2x+1\right)\)
\(\Rightarrow x^2-2x=2x^2+x\)
\(\Rightarrow x^2-2x^2=x+2x\)
\(\Rightarrow-x^2=3x\)
\(\Rightarrow-x^2-3x=0\)
\(\Rightarrow x\left(-x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)
Vậy...
b/\(\dfrac{x}{2}\left(x-2\right)=\left(x-2\right)\left(3x+1\right)\)
\(\Rightarrow\dfrac{x^2}{2}-x=3x^2+x-6x-2\)
\(\Rightarrow\dfrac{x^2}{2}-x=3x^2-5x-2\)
\(\Rightarrow\dfrac{x^2}{2}-3x^2=-5x+x-2\)
\(\Rightarrow-\dfrac{5}{2}x^2=-4x-2\)
\(\Rightarrow-\dfrac{5}{2}x^2+4x+2=0\)
\(\Rightarrow5x^2-8x-4=0\)
\(\Rightarrow\left(5x^2-10x\right)+\left(2x-4\right)=0\)
\(\Rightarrow5x\left(x-2\right)+2\left(x-2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(5x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{2}{5}\end{matrix}\right.\)
Vậy...
c/\(3x\left(x-2\right)=4x-8\)
\(\Rightarrow3x^2-6x=4x-8\)
\(\Rightarrow-6x+3x^2=4x-8\)
\(\Rightarrow-6x-4x=-8-3x^2\)
\(\Rightarrow-10x=-8-3x^2\)
\(\Rightarrow-10x+8+3x^2=0\)
\(\Rightarrow3x^2-10x+8=0\)
\(\Rightarrow\left(3x^2-4x\right)-\left(6x-8\right)=0\)
\(\Rightarrow x\left(3x-4\right)-2\left(3x-4\right)=0\)
\(\Rightarrow\left(3x-4\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=2\end{matrix}\right.\)
Vậy...
d/\(\dfrac{x}{3}-1=x\left(x-3\right)\)
\(\Rightarrow\dfrac{x}{3}-1=x^2-3x\)
\(\Rightarrow-1+\dfrac{x}{3}=x^2-3x\)
\(\Rightarrow-1-x^2=-3x-\dfrac{x}{3}\)
\(\Rightarrow-1-x^2=-\dfrac{10}{3}x\)
\(\Rightarrow-1-x^2+\dfrac{10}{3}x=0\)
\(\Rightarrow-x^2+\dfrac{10}{3}x-1=0\)
\(\Rightarrow3x^2-10x+3=0\)
\(\Rightarrow\left(3x^2-x\right)-\left(9x-3\right)=0\)
\(\Rightarrow x\left(3x-1\right)-3\left(3x-1\right)=0\)
\(\Rightarrow\left(3x-1\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=3\end{matrix}\right.\)
Vậy
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