Question

giải phương trình \(x^3+\dfrac{x^3}{\left(x-1\right)^3}+\dfrac{3x^2}{x-1}=2\\\)

Answer 1

Đk : x khác 1

pt đã cho \(\Leftrightarrow x^3\left(x-1\right)^3+x^3+3x^2\left(x-1\right)^2=2\left(x-1\right)^3\)

\(\Leftrightarrow4x^4-10x^3+12x^2-8x+2=0\)

\(\Leftrightarrow\left(x-1\right)\left(4x^3-6x^2+6x-2\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(L\right)\\x=\dfrac{1}{2}\left(N\right)\end{matrix}\right.\)

kl: x=1/2