Question

Giải phương trình: 9(4x+3)^2=4(x^2-2x+1)

help

Answer 1

\(\Leftrightarrow\left(12x+9\right)^2-\left(2x-2\right)^2=0\)

\(\Leftrightarrow\left(12x+9-2x+2\right)\left(12x+9+2x-2\right)=0\)

\(\Leftrightarrow\left(10x+11\right)\left(14x+7\right)=0\)

=>x=-11/10 hoặc x=-1/2

Answer 2

\(9\left(4x+3\right)^2=4\left(x^2-2x+1\right)\\ \Leftrightarrow\left[3\left(4x+3\right)\right]^2-4\left(x-1\right)^2=0\\ \Leftrightarrow\left(12x+9\right)^2-\left[2\left(x-1\right)\right]^2=0\\ \Leftrightarrow\left(12x+9\right)^2-\left(2x-2\right)^2=0\\ \Leftrightarrow\left(12x+9-2x+2\right)\left(12x+9+2x-2\right)=0\\ \Leftrightarrow\left(10x+11\right)\left(14x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-11}{10}\\x=\dfrac{-1}{2}\end{matrix}\right.\)