a,\(x^3-x=0\Rightarrow x\left(x^2-1\right)=0\Rightarrow x\left(x+1\right)\left(x-1\right)=0\)
b,\(x^2-2x+x-2=0\Rightarrow x\left(x-2\right)+\left(x-2\right)=0\Rightarrow\left(x-2\right)\left(x+1\right)=0\)
c,\(x^2-6x+8=x^2-4x-2x+8=x\left(x-4\right)-2\left(x-4\right)=\left(x-4\right)\left(x-2\right)\)
\(x^3-x=0\)
\(\Leftrightarrow x\left(x^2-1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)=0\)
x=0 hoặc x-1=0=> x=1 hoặc x+1=0 => x=-1
\(x^2-2x+x-2=0\)
\(\Leftrightarrow x\left(x-2\right)+\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x+1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}}\)
\(x^2-6x+8=0\)
\(\Leftrightarrow x^2-2x-4x+8=0\)
\(\Leftrightarrow x\left(x-2\right)-4\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x-4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=4\end{cases}}}\)
a) x3 - x = 0
x.(x2 - 1) = 0
x.(x+1).(x-1) = 0
=> x = 0; x = -1;x = 1
b) x2 - 2x + x - 2= 0
x.(x-2) + (x-2) = 0
(x-2).(x+1) = 0
=> x = 2; x = -1
c) x2 -6x + 8 = 0
x2 - 2x - 4x + 8 0
x.(x-2) - 4.(x-2) = 0
(x-2).(x-4) =0
=> x = 2; x = 4
\(x^3-x=0\Leftrightarrow x\left(x^2-1\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x^2-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x^2=1\end{cases}\Rightarrow}\hept{\begin{cases}x=1\\x=0\\x=-1\end{cases}}}\)
\(x^2-2x+x-2=0\)
\(x^2-\left(2x-x+2\right)=0\)
\(\Leftrightarrow x^2=2x-x+2\)
\(x^2=x+2\)
\(\Leftrightarrow x=2\)
\(x^2-6x+8=0\)
\(x^2-\left(6x-8\right)=0\)
\(\Leftrightarrow x^2=6x-8\)
\(xx-6x=-8\)
\(x.\left(x-6\right)=-8\)
\(x=\frac{-8}{x-6}\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=4\end{cases}}\)
