\(\left(\frac{1}{2x}-1004\right)^{2008}=\left(\frac{1}{2x}-1004\right)^{2006}\)
\(\Rightarrow\left(\frac{1}{2x}-1004\right)^{2008}-\left(\frac{1}{2x}-1004\right)^{2006}=0\)
\(\Rightarrow\left(\frac{1}{2x}-1004\right)^{2006}.\left(\frac{1}{2x}-1004\right)^2-\left(\frac{1}{2x}-1004\right)^{2006}=0\)
\(\Rightarrow\left(\frac{1}{2x}-1004\right)^{2006}.\left[\left(\frac{1}{2x}-1004\right)^2-1\right]=0\)
\(\Rightarrow\left(\frac{1}{2x}-1004\right)^{2006}=0\) hoặc \(\left(\frac{1}{2x}-1004\right)^2-1=0\)
TH1: \(\left(\frac{1}{2x}-1004\right)^{2006}=0\)
\(\Rightarrow\frac{1}{2x}-1004=0\)
\(\Rightarrow\frac{1}{2x}=1004\)
\(\Rightarrow2x=1:1004=\frac{1}{1004}\)
\(\Rightarrow x=\frac{1}{2008}\)
TH2: \(\left(\frac{1}{2x}-1004\right)^2-1=0\)
\(\Rightarrow\left(\frac{1}{2x}-1004\right)^2=1\)
\(\Rightarrow\frac{1}{2x}-1004=1\) hoặc \(\frac{1}{2x}-1004=-1\)
\(\Rightarrow\frac{1}{2x}=1005\) hoặc \(\frac{1}{2x}=1003\)
\(\Rightarrow x=\frac{1}{2010}\) hoặc \(x=\frac{1}{2006}\)
Vậy \(x\in\left\{\frac{1}{2010};\frac{1}{2008};\frac{1}{2006}\right\}\)
