a)\(x^2-3x=0\)
\(\Leftrightarrow x\left(x-3\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
b)\(x^5-9x=0\)
\(\Leftrightarrow x\left(x^4-9\right)=0\)
\(\Leftrightarrow x\left(x^2+3\right)\left(x^2-3\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x^2+3=0\\x^2-3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x\in\varnothing\\x=\pm\sqrt{3}\end{matrix}\right.\)
c)\(\left(x^3-4x^2\right)-\left(x-4\right)=0\)
\(\Leftrightarrow x^2\left(x-4\right)-\left(x-4\right)=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-1\right)\left(x-4\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x+1=0\\x-1=0\\x-4=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-1\\x=1\\x=4\end{matrix}\right.\)
d)\(\left(4x^2-25\right)^2-9\left(2x-5\right)^2=0\)
\(\Leftrightarrow\left(2x+5\right)^2\left(2x-5\right)^2-3\left(2x-5\right)^2=0\)
\(\Leftrightarrow\left(2x-5\right)^2\left(4x^2+10x+5-3\right)=0\)
\(\Leftrightarrow\left(2x-5\right)^2\left(4x^2+4x+2x+2\right)=0\)
\(\Leftrightarrow\left(2x-5\right)^2\left[4x\left(x+1\right)+2\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(2x-5\right)^2.2\left(2x+1\right)\left(x+1\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}2x-5=0\\2x+1=0\\x+1=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}=2,5\\x=-\dfrac{1}{2}=-0,5\\x=-1\end{matrix}\right.\)
