Question

Giair pt sau : \(x^2-x-\frac{1}{x}+\frac{1}{x^2}-10=0\)

Answer 1

\(x^2-x-\frac{1}{x}+\frac{1}{x^2}-10=0\Leftrightarrow\frac{x^4-x^3-10x^2-x+1}{x^2}=0\)\(\Leftrightarrow x^4-x^3-10x^2-x+1=0\)

\(\Leftrightarrow\left(x^4-4x^3+x^2\right)+\left(3x^3-12x+3x\right)+\left(x^2-4x+1\right)=0\)

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

\(\Leftrightarrow\left(x^2+3x+1\right)\left(x^2-4x+1\right)=0\Leftrightarrow\orbr{\begin{cases}x^2+3x+1=0\\x^2-4x+1=0\end{cases}}\)

giải từng trường hợp là ra nghiệm