Question

Giải PT: 3(x-1)(2x-1)=5(x+9)(x-1)

Answer 1

\(3\left(2x-1\right)=5\left(x+9\right)\)

\(\Leftrightarrow6x-3-5x-45=0\)

\(\Leftrightarrow x-48=0\)

\(\Leftrightarrow x=48\)

Answer 2

\(3\left(x-1\right)\left(2x-1\right)=5\left(x+9\right)\left(x-1\right)\\ \Leftrightarrow\left[3\left(2x-1\right)\right]\left(x-1\right)=\left[5\left(x+9\right)\right]\left(x-1\right)\\ \Leftrightarrow\left(6x-3\right)\left(x-1\right)=\left(5x+45\right)\left(x-1\right)\\ \Leftrightarrow\left(6x-3\right)\left(x-1\right)-\left(5x+45\right)\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(6x-3-5x-45\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-48\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-48=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=48\end{matrix}\right.\)

Vậy phương trình có tập nghiệm `S={1;48}`