Question

Tìm x biết:

\(a.\left|2x-3\right|=x-2\\ b.\left(2x+3\right)^6-\left(2x+3\right)^4=0\)

Answer 1

b) \(\left(2x+3\right)^6-\left(2x+3\right)^4=0\)

\(\left(2x+3\right)^4.\left[\left(2x+3\right)^2-1\right]=0\)

\(\left(2x+3\right)^4.\left(2x+3-1\right)\left(2x+3+1\right)=0\)

\(\left(2x+3\right)^4.\left(2x+2\right)\left(2x+4\right)=0\)

\(\Rightarrow\left(2x+3\right)^4=0\)  hoac  \(\orbr{\begin{cases}2x+2=0\\2x+4=0\end{cases}}\)

\(\Rightarrow2x+3=0\)  hoac  \(\orbr{\begin{cases}2x=-2\\2x=-4\end{cases}}\)

\(\Rightarrow x=\frac{-3}{2}\) hoac \(\orbr{\begin{cases}x=-1\\x=-2\end{cases}}\)

       vay \(x=\frac{-3}{2}\) hoac \(\orbr{\begin{cases}x=-1\\x=-2\end{cases}}\)