Question

giải phương trình: x^3-1=-x(x-1)

Answer 1

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

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

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

=>x=1 hoặc x=-1

Answer 2

\(x^3-1=-x\left(x-1\right)\)

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)