Question

(2x -1 )² = 3x.(2x - 1)

Answer 1

\(\left(2x-1\right)^2=3\left(2x-1\right)\)

\(\Leftrightarrow\left(2x-1\right)^2-3x\left(2x-1\right)=0\)

\(\Leftrightarrow\left(2x-1\right)^3\left(1-3x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^3=0\\1-3x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)

Vậy phương trình có nghiệm \(x=\dfrac{1}{2}\) hoặc \(x=\dfrac{1}{3}\)

Answer 2

ta có: (2x-1)(2x-1-3x)=0

\(\Leftrightarrow\)(2x-1)(-x-1)=0

\(\Leftrightarrow\)x=\(\dfrac{1}{2}\); x=-1