Question

Tìm x thoả mãn: \(x^5=x^4+x^3+x^2+x+2\)

Answer 1

\(\Leftrightarrow x^5-1=x^4+x^3+x^2+x+1\)

\(\Leftrightarrow\left(x-1\right)\left(x^4+x^3+x^2+x+1\right)=x^4+x^3+x^2+1\)

\(\Leftrightarrow\left(x-2\right)\left(x^4+x^3+x^2+x+1\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left[\left(x^2+\dfrac{x}{2}\right)^2+\dfrac{3}{4}\left(x+\dfrac{2}{3}\right)^2+\dfrac{2}{3}\right]=0\)

\(\Leftrightarrow x=2\)