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If `alpha,beta` are roots of the equation `x^(2)+5(sqrt(2))x+10=0,alphagtbetaandP_(n)=alpha^(n)-beta^(n)` for each positive integer n , then the value of `((P_(17)P_(20)+5sqrt(2)P_(17)P_(19))/(P_(18)P_(19)+5sqrt(2)P_(18)^(2)))` is equal to ________.

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