*\(\left(2x-3\right)^2=\left(x+5\right)^2\)
\(\Rightarrow\left(2x-3\right)^2-\left(x+5\right)^2=0\)
\(\Rightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)
\(\Rightarrow\left(x-8\right)\left(3x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)
* \(x^3-16x=0\)
\(\Rightarrow x\left(x^2-16\right)=0\)
\(\Rightarrow x\left(x^2-4^2\right)=0\)
\(\Rightarrow x\left(x-4\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
*\(x^4-2x^3+10x^2-20x=0\)
\(\Rightarrow\left(x^4+10x^2\right)-\left(2x^3+20x\right)=0\)
\(\Rightarrow x^2\left(x^2+10\right)-2x\left(x^2+10\right)=0\)
\(\Rightarrow\left(x^2+10\right)\left(x^2-2x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\varnothing\\x=2\end{matrix}\right.\)
\(x^3-16x=0\)
\(\Leftrightarrow x\left(x-4\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
2) \(x^4-2x^3+10x^2-20x=0\)
\(\Leftrightarrow x^3\left(x-2\right)+10x\left(x-2\right)=0\)
\(\Leftrightarrow x\left(x-2\right)\left(x^2+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-2=0\\x^2+10=0\left(ktm\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
3)\(\left(2x-3\right)^2=\left(x+5\right)^2\)
\(\Leftrightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)
\(\Leftrightarrow\left(x-8\right)\left(3x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-8=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)
4) \(x^2\left(x-1\right)-4x^2+8x-4=0\)
\(\Leftrightarrow x^2\left(x-1\right)-\left(2x-2\right)^2=0\)
\(\Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-4\left(x-1\right)\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
* \(x^2\left(x-1\right)-4x^2+8x-4=0\)
\(\Rightarrow x^2\left(x-1\right)-4\left(x^2-2x+1\right)=0\)
\(\Rightarrow x^2\left(x-1\right)-4\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^2-4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
*x2 (x - 1) - 4x2+ 8x - 4 = 0
⇒x2 (x-1) - 4 ( x2 - 2x + 1) = 0
⇒x2 (x - 1) - 4x - 1 = 0
⇒(x - 1) (x2 - 4) = 0
⇒x=1;x=2