Question

tìm x 

(x^3-1):(x^2+x+1)=x^2-2x-1

Answer 1

Có: \(\left(x^3-1\right):\left(x^2+x+1\right)=x^2-2x-1\)

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

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

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

\(\Rightarrow\left(x-1\right)\left[1-\left(x-1\right)\right]=0\)

\(\Rightarrow\left(x-1\right)\left(2-x\right)=0\) \(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

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