If \( \alpha ,\beta \) are roots of the equation \( x^{2}+5(\sqrt{2})\,x+10=0 \), \( \alpha>\beta \) and \( P_{n}=\alpha^{n}-\beta^{n} \) for each positive integer \( n \), then the value of \( \left( \dfrac{P_{17}P_{20}+5\sqrt{2}\,P_{17}P_{19}}{P_{18}P_{19}+5\sqrt{2}\,P_{18}^{2}} \right) \) is equal to __________ .
