Question

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

 

Answer 1

ĐK: \(x\ne1\)

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

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

\(\Leftrightarrow\left[\left(x-1\right)^2+1\right]\left[\left(x^2-\frac{x}{2}\right)^2+\frac{3x^2}{4}+\left(x+1\right)^2\right]=0\)

\(\Leftrightarrow x^2-\frac{x}{2}=x=x+1=0\text{ (vô nghiệm)}\)

Vậy pt vô nghiệm.