Question

[Song Tử Gemini]

Tìm x biết: (1/2x-1004)^2008 = (1/2x-1004)^2006 a c giúp e với

Answer 1

[Lovers]

\(\left(\frac{1}{2x}-1004\right)^{2008}=\left(\frac{1}{2x}-1004\right)^{2006}\)

\(\Rightarrow\left(\frac{1}{2x}-1004\right)^{2008}-\left(\frac{1}{2x}-1004\right)^{2006}=0\)

\(\Rightarrow\left(\frac{1}{2x}-1004\right)^{2006}.\left(\frac{1}{2x}-1004\right)^2-\left(\frac{1}{2x}-1004\right)^{2006}=0\)

\(\Rightarrow\left(\frac{1}{2x}-1004\right)^{2006}.\left[\left(\frac{1}{2x}-1004\right)^2-1\right]=0\)

\(\Rightarrow\left(\frac{1}{2x}-1004\right)^{2006}=0\) 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 \(x\in\left\{\frac{1}{2010};\frac{1}{2008};\frac{1}{2006}\right\}\)

Answer 2

[Song Tử Gemini]

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