Bài 13:
a: Ta có: \(\left(x-5\right)-4x+20=0\)
\(\Leftrightarrow x-5=0\)
hay x=5
b: Ta có: \(x\left(x+6\right)-7x-42=0\)
\(\Leftrightarrow\left(x+6\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=7\end{matrix}\right.\)
c: Ta có: \(x^3-5x^2+x-5=0\)
\(\Leftrightarrow\left(x-5\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow x-5=0\)
hay x=5
d: Ta có: \(x^4-2x^3+10x^2-20x=0\)
\(\Leftrightarrow x\left(x^3-2x^2+10x-20\right)=0\)
\(\Leftrightarrow x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
Bài 13:
a) \(\left(x-5\right)-4x+20=0\\ \Rightarrow\left(x-5\right)-\left(4x-20\right)=0\\ \Rightarrow\left(x-5\right)-4\left(x-5\right)=0\\ \Rightarrow-3\left(x-5\right)=0\\ \Rightarrow x-5=0\\ \Rightarrow x=5\)
b) \(x\left(x+6\right)-7x-42=0\\ \Rightarrow x\left(x+6\right)-\left(7x+42\right)=0\\ \Rightarrow x\left(x+6\right)-7\left(x+6\right)=0\\ \Rightarrow\left(x+6\right)\left(x-7\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+6=0\\x-7=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-6\\x=7\end{matrix}\right.\)
c) \(x^3-5x^2+x-5=0\\ \Rightarrow\left(x^3-5x^2\right)+\left(x-5\right)=0\\ \Rightarrow x^2\left(x-5\right)+\left(x-5\right)=0\\ \Rightarrow\left(x-5\right)\left(x^2-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x^2-1=0\\x-5=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=1\\x=5\end{matrix}\right.\)
d) \(x^4-2x^3+10x^2-20x=0\\ \Rightarrow\left(x^4-2x^3\right)+\left(10x^2-20x\right)=0\\ \Rightarrow x^3\left(x-2\right)+10x\left(x-2\right)=0\\ \Rightarrow\left(x^3+10x\right)\left(x-2\right)=0\\ \Rightarrow x\left(x^2+10\right)\left(x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^2+10=0\\x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^2=-10\left(loại\right)\\x=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
