\(a,x^3-25x=0\\ \Leftrightarrow x\left(x^2-25\right)=0\\ \Leftrightarrow x\left(x-5\right)\left(x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)
\(b,x^4+4=5x^2\\ \Leftrightarrow x^4-5x^2+4=0\\ \Leftrightarrow x^4-4x^2-x^2+4=0\\ \Leftrightarrow x^2\left(x^2-4\right)-\left(x^2-4\right)=0\\ \Leftrightarrow\left(x^2-1\right)\left(x^2-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2=1\\x^2=4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\pm1\\x=\pm2\end{matrix}\right.\)
\(c,x^3+27+x^2-6x-27=0\\ \Leftrightarrow x\left(x^2+x-6\right)=0\\ \Leftrightarrow x\left(x^2+3x-2x-6\right)=0\\ \Leftrightarrow x\left[x\left(x+3\right)-2\left(x+3\right)\right]=0\\ \Leftrightarrow x\left(x-2\right)\left(x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-3\end{matrix}\right.\)
\(d,4\left(x-2\right)^2=25\left(1-2x\right)^2\\ \Leftrightarrow\left(2x-4\right)^2=\left(5-10x\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}2x-4=5-10x\\2x-4=10x-5\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}12x=9\\8x=1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{1}{8}\end{matrix}\right.\)
\(e,\left(3x-5\right)\left(2x-1\right)-\left(x+2\right)\left(6x-1\right)=0\\ \Leftrightarrow6x^2-13x+5-6x^2-11x+2=0\\ \Leftrightarrow-24x=-7\\ \Leftrightarrow x=\dfrac{7}{24}\)
\(f,\left(3x+2\right)\left(3x-2\right)-\left(3x-1\right)^2=5\\ \Leftrightarrow9x^2-4-9x^2+6x-1-5=0\\ \Leftrightarrow6x=10\\ \Leftrightarrow x=\dfrac{5}{3}\)
