a: \(\left(x-1\right)^3=27\)
=>\(\left(x-1\right)^3=3^3\)
=>x-1=3
=>x=3+1=4
b: \(x^2+x=0\)
=>x(x+1)=0
=>\(\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
c: \(\left(2x+1\right)^2=25\)
=>\(\left[{}\begin{matrix}2x+1=5\\2x+1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=4\\2x=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
d: \(\left(2x-1\right)^3=36\)
=>\(2x-1=\sqrt[3]{36}\)
=>\(2x=\sqrt[3]{36}+1\)
=>\(x=\dfrac{\sqrt[3]{36}+1}{2}\)
e: \(5^{x+2}=625\)
=>\(5^{x+2}=5^4\)
=>x+2=4
=>x=2
f: \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
=>\(\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\)
=>\(\left(x-1\right)^{x+2}\cdot\left(x-1-1\right)\left(x-1+1\right)=0\)
=>\(\left(x-1\right)^{x+2}\cdot x\cdot\left(x-2\right)=0\)
=>\(x\in\left\{0;1;2\right\}\)
g: \(\left(2x-1\right)^3=-8\)
=>2x-1=-2
=>2x=-1
=>\(x=-\dfrac{1}{2}\)
