\(a)\left(2x+1\right)^2=25\)
\(\Rightarrow\left(2x+1\right)^2=\left(\pm5\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}2x+1=5\\2x+1=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=4\\2x=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
\(\left(2x-3\right)^2=36\)
\(\Rightarrow\left(2x-3\right)^2=\left(\pm6\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}2x-3=6\\2x-3=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=9\\2x=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{9}{2}\\x=-\frac{3}{2}\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=\frac{9}{2}\\x=-\frac{3}{2}\end{matrix}\right.\)
\(b)5^x+2=625\)
\(\Rightarrow5^x=623\)
\(\Rightarrow x\in\varnothing\)
Vậy \(x\in\varnothing\)
\(\left(2x-1\right)^3=-8\)
\(\Rightarrow\left(2x-1\right)^3=\left(-2\right)^3\)
\(\Rightarrow2x-1=-2\)
\(\Rightarrow2x=-1\)
\(\Rightarrow x=-\frac{1}{2}\)