\(x^2+x=0\)
\(\Rightarrow x\left(x+1\right)=0\)
\(\Rightarrow x=0\)
\(\Rightarrow x+1=0\Rightarrow x=-1\)
\(\left(2x+1\right)^2=25\)
\(\Rightarrow\left(2x+1\right)^2=\pm5^2\)
\(\Rightarrow2x+1=5\Rightarrow2x=4\Rightarrow x=2\)
\(\Rightarrow2x+1=-5\Rightarrow2x=-6\Rightarrow x=-3\)
\(\left(2x-3\right)^2=36\)
\(\Rightarrow\left(2x-3\right)^2=\pm6^2\)
\(\Rightarrow2x-3=6\Rightarrow2x=9\Rightarrow x=\dfrac{9}{2}\)
\(\Rightarrow2x-3=-6\Rightarrow2x=-3\Rightarrow x=\dfrac{-3}{2}\)
\(5^{x+2}=625\)
\(\Rightarrow5^{x+2}=5^4\)
\(\Rightarrow x+2=4\Rightarrow x=2\)
\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
\(\Rightarrow x+2\ne x+4\)
\(\Rightarrow x-1\in\left\{0;\pm1\right\}\)
\(\Rightarrow x\in\left\{0;1;2\right\}\)
a) \(x^2+x=0\)
\(\Rightarrow x\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
Vậy x=-1 hoặc 0
c) \(\left(2x+1\right)^2=25\)
\(\Leftrightarrow\left(2x+1\right)^2-25=0\)
\(\Leftrightarrow\left(2x+1\right)^2-5^2=0\)
\(\Leftrightarrow\left(2x+1-5\right)\left(2x+1+5\right)=0\)
\(\Leftrightarrow\left(2x-4\right)\left(2x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-4=0\\2x+6=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=4\\2x=-6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
Vậy x=2 hoặc x=-3
d) \(\left(2x-3\right)^2=36\)
\(\Leftrightarrow\left(2x-3\right)^2-36=0\)
\(\Leftrightarrow\left(2x-3\right)^2-6^2=0\)
\(\Leftrightarrow\left(2x-3-6\right)\left(2x-3+6\right)=0\)
\(\Leftrightarrow\left(2x-9\right)\left(2x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-9=0\\2x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=9\\2x=-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=\dfrac{-3}{2}\end{matrix}\right.\)
Vậy \(x=\dfrac{9}{2}\) hoặc \(x=\dfrac{-3}{2}\)
e) \(5^{x+2}=625\)
\(\Leftrightarrow5^{x+2}=5^4\)
\(\Leftrightarrow x+2=4\)
\(\Leftrightarrow x=2\)
Vậy x=2
