\(x+\dfrac{1}{x}=3\\ \Leftrightarrow\left(x+\dfrac{1}{x}\right)^3=27\\ \Leftrightarrow x^3+\dfrac{1}{x^3}+3\left(x+\dfrac{1}{x}\right)=27\\ \Leftrightarrow x^3+\dfrac{1}{x^3}+9=27\\ \Leftrightarrow x^3+\dfrac{1}{x^3}=18\)
\(x+\dfrac{1}{x}=3\\ \Leftrightarrow x^2+2+\dfrac{1}{x^2}=9\\ \Leftrightarrow x^2+\dfrac{1}{x^2}=7\)
\(\Rightarrow\left(x^3+\dfrac{1}{x^3}\right)\left(x^2+\dfrac{1}{x^2}\right)=126\\ \Rightarrow x^5+x+\dfrac{1}{x}+\dfrac{1}{x^5}=126\\ \Leftrightarrow x^5+\dfrac{1}{x^5}=123\)
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