Problem

\( \begin{array}{c}x^{(x-1)^{2}}=2 x+1 \\ x-\frac{1}{x}=?\end{array} \)

Answer

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Answer

\(x-\frac{1}{x}=2-\frac{1}{2}=\frac{3}{2}\)

Steps

Step 1 :\(x^{(x-1)^{2}}-2x-1=0\)

Step 2 :\(u=x-1\)

Step 3 :\(x=u+1\)

Step 4 :\((u+1)^{u^{2}}-2(u+1)-1=0\)

Step 5 :\(u=1\)

Step 6 :\(x=2\)

Step 7 :\(x-\frac{1}{x}=2-\frac{1}{2}=\frac{3}{2}\)

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