Question

[phan bích ngọc]

( 3x - 2 )^2004= ( 3x - 2 )^2006

Answer 1

[Nguyễn Lê Phước Thịnh]

\(\left(3x-2\right)^{2004}=\left(3x-2\right)^{2006}\)

=>\(\left(3x-2\right)^{2006}-\left(3x-2\right)^{2004}=0\)

=>\(\left(3x-2\right)^{2004}\left[\left(3x-2\right)^2-1\right]=0\)

=>\(\left(3x-2\right)^{2004}\cdot\left(3x-3\right)\left(3x-1\right)=0\)

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

Answer 2

[HT.Phong (9A5)]

\(\left(3x-2\right)^{2004}=\left(3x-2\right)^{2006}\\ =>\left(3x-2\right)^{2006}-\left(3x-2\right)^{2004}=0\\ =>\left(3x-2\right)^{2004}\left[\left(3x-2\right)^2-1\right]=0\)

+) \(\left(3x-2\right)^{2004}=0=>3x-2=0=>x=\dfrac{2}{3}\)

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

\(TH1:3x-2=1=>3x=1+2=3=>x=\dfrac{3}{3}=1\\ TH2:3x-2=-1=>3x=-1+2=1=>x=\dfrac{1}{3}\)