ĐKXĐ: ...
a/ Đặt \(x+\frac{1}{x}=t\Rightarrow x^2+\frac{1}{x^2}=t^2-2\)
\(t=t^2-2\Leftrightarrow t^2-t-2=0\Rightarrow\left[{}\begin{matrix}t=-1\\t=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x+\frac{1}{x}=-1\\x+\frac{1}{x}=2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2+x+1=0\left(vn\right)\\x^2-2x+1=0\end{matrix}\right.\) \(\Rightarrow x=1\)
b/ \(\Leftrightarrow\left(\frac{1}{x}+2\right)\left(x^2+2\right)-\left(\frac{1}{x}+2\right)=0\)
\(\Leftrightarrow\left(\frac{1}{x}+2\right)\left(x^2+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\frac{1}{x}+2=0\\x^2+1=0\left(vn\right)\end{matrix}\right.\) \(\Rightarrow\frac{1}{x}=-2\Rightarrow x=-\frac{1}{2}\)
c/ \(\Leftrightarrow\left(x+1+\frac{1}{x}\right)^2-\left(x-1-\frac{1}{x}\right)^2=0\)
\(\Leftrightarrow2x\left(2+\frac{2}{x}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\2+\frac{2}{x}=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\left(l\right)\\x=-1\end{matrix}\right.\)
