[tex]\it x+\dfrac{1}{x}=3 \Rightarrow \left(x+\dfrac{1}{x}\right)^3=3^3 \Rightarrow x^3+\dfrac{1}{x^3}+3x\cdot\dfrac{1}{x} \left(x+\dfrac{1}{x}\right) =27 \Rightarrow
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\Rightarrow x^3+\dfrac{1}{x^3}+3 \cdot1\cdot3=27 \Rightarrow x^3+\dfrac{1}{x^3}+9=27|_{-9} \Rightarrow x^3+\dfrac{1}{x^3}= 18
[/tex]
