\(9+\sqrt{80}=\dfrac{72+32\sqrt{5}}{8}=\dfrac{27+3.3^2.\sqrt{5}+3.3.5+5\sqrt{5}}{8}=\dfrac{\left(3+\sqrt{5}\right)^3}{8}\)
\(=\left(\dfrac{3+\sqrt{5}}{2}\right)^3\)
\(\Rightarrow\sqrt[3]{9+\sqrt{80}}=\dfrac{3+\sqrt{5}}{2}\)
\(\Rightarrow P=\left(\dfrac{3+\sqrt{5}}{2}\right)^{2017}.\left(3-\dfrac{3+\sqrt{5}}{2}\right)^{2018}\)
\(=\left(\dfrac{3+\sqrt{5}}{2}\right)^{2017}.\left(\dfrac{3-\sqrt{5}}{2}\right)^{2018}\)
\(=\left[\dfrac{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}\right]^{2017}\left(\dfrac{3-\sqrt{5}}{2}\right)\)
\(=1^{2017}.\left(\dfrac{3-\sqrt{5}}{2}\right)=\dfrac{3-\sqrt{5}}{2}\)
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