Question

Giải: \(x^2-x-\dfrac{1}{x}+\dfrac{1}{x^2}-10=0\)

Answer 1

ĐK: x khác 0

Ta có pt tương đương \(x^2+2+\dfrac{1}{x^2}-\left(x+\dfrac{1}{x}\right)-12=0\)

<=>\(\left(x+\dfrac{1}{x}\right)^2-\left(x+\dfrac{1}{x}\right)-12=0\)

<=>\(\left[{}\begin{matrix}x+\dfrac{1}{x}=-3\\x+\dfrac{1}{x}=4\end{matrix}\right.\)

<=>\(\left[{}\begin{matrix}x^2+3x+1=0\left(1\right)\\x^2-4x+1=0\left(2\right)\end{matrix}\right.\)

Ta thấy pt (1)vô nghiệm

Pt(2) <=>\(\left[{}\begin{matrix}x=2+\sqrt{3}\\x=2-\sqrt{3}\end{matrix}\right.\)

KL \(x=2+\sqrt{3}\), \(x=2-\sqrt{3}\)