a, \(\left(x+1\right)^2=3\left(x+1\right)\)
\(\Rightarrow\left(x+1\right)^2-3\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right).\left(x+1-3\right)=0\)
\(\Rightarrow\left(x+1\right).\left(x-2\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x+1=0\\x-2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
Vậy \(x\in\left\{-1;2\right\}\)
b, \(\left(2x-7\right)^3=8\left(7-2x\right)^2\)
\(\Rightarrow\left(2x-7\right)^3-8\left(2x-7\right)^2=0\) (do \(\left[A\left(x\right)\right]^2=\left[-A\left(x\right)\right]^2\))
\(\Rightarrow\left(2x-7\right)^2.\left(2x-7-8\right)=0\)
\(\Rightarrow\left(2x-7\right)^3.\left(2x-15\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}\left(2x-7\right)^3=0\\2x-15=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x-7=0\\2x=15\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=7\\x=7,5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=3,5\\x=7,5\end{matrix}\right.\)
Vậy \(x\in\left\{3,5;7,5\right\}\)
Chúc bạn học tốt!!!
