Question

x^4-x^3+x^2-x=0

Answer 1

\(x^4-x^3+x^2-x=0\\ x\left(x^3-x^2+x-1\right)=0\\ x\left[x^2\left(x-1\right)+\left(x-1\right)\right]=0\\ x\left(x^2+1\right)\left(x-1\right)=0\\ \left[{}\begin{matrix}x=0\\x^2+1=0\\x-1=0\end{matrix}\right.\left[{}\begin{matrix}x=0\\x^2=-1\left(voli\right)\\x=1\end{matrix}\right.\\ x\in\left\{0;1\right\}\)

Answer 2

`x^4-x^3+x^2-x=0`

`<=> x^3(x-1) + x (x-1) =0`

`<=> (x^3+x)(x-1) =0`

`<=> x(x^2 +1)(x-1) =0`

`<=> [(x=0),(x^2 +1 =0),(x-1=0):}`

`<=> [(x=0,(x^2=-1(vô-lí)),(x=1):}`

Vậy `S={0;1}`