Question

Giải phương trình: \(x^3+\dfrac{x^3}{\left(x-1\right)^3}+\dfrac{3x^2}{x-1}-2=0\).

Answer 1

ĐKXĐ: \(x\ne1\)

\(x^3+\left(\dfrac{x}{x-1}\right)^3+\dfrac{3x^2}{x-1}-2=0\)

\(\Leftrightarrow\left(x+\dfrac{x}{x-1}\right)^3-3x.\dfrac{x}{x-1}\left(x+\dfrac{x}{x-1}\right)+\dfrac{3x^2}{x-1}-2=0\)

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

\(\Leftrightarrow\left(\dfrac{x^2}{x-1}-1\right)^3=1\)

\(\Leftrightarrow\dfrac{x^2}{x-1}-1=1\)

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

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

Pt đã cho vô nghiệm