Question

(3x-5)^2-4(x-3)^2=0 giải phương trình

Answer 1

\(\left(3x-5\right)^2-4\left(x-3\right)^2=0\\ \Leftrightarrow\left(3x-5\right)^2-\left[2\left(x-3\right)\right]^2=0\\ \Leftrightarrow\left(3x-5\right)^2-\left(2x-6\right)^2=0\\ \Leftrightarrow\left(3x-5-2x+6\right)\left(3x-5+2x-6\right)=0\\ \Leftrightarrow\left(x+1\right)\left(5x-11\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+1=0\\5x-11=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{11}{5}\end{matrix}\right.\)

Answer 2

\(\Leftrightarrow\left(3x-5\right)^2-\left(2x-6\right)^2=0\)

\(\Leftrightarrow\left(3x-5-2x+6\right)\left(3x-5+2x-6\right)=0\)

=>(x+1)(5x-11)=0

=>x=-1 hoặc x=11/5