Question

Giải phương trình:

\(x^3-x^2+x-1=0\)

Answer 1

\(x^3-x^2+x-1=0\)

\(\Leftrightarrow x^2\left(x-1\right)+\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^2+1\right)=0\)

Dễ thấy: \(x^2\ge0\forall x\)

\(\Rightarrow x^2+1\ge1>0\forall x\) (vô nghiệm)

Nên \(x-1=0\Rightarrow x=1\)

Answer 2

$x^3-x^2+x-1=0$

\(\Rightarrow x^2\left(x-1\right)+\left(x-1\right)=0\)

\(\Rightarrow\left(x-1\right)\left(x^2+1\right)=0\)

Vì \(x^2+1>0\)

\(\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

S = {1}

Answer 3