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 ({{P}_{17} {P}_{20}+5 \\sqrt{2} {P}_{17} {P}_{19}}/{{P}_{18} {P}_{19}+5 \\sqrt{2} {P}_{18}^{2}}) is equal to ________. [25 Jul 2021 Shift 1]

Quadratic Equation and Inequalities Part 1

Section: Mathematics

Question : 13 of 100

Marks: +1, -0

If α,β are roots of the equation x2+5(√2)x+10=0,α>β and Pn=αn−βn for each positive integer n, then the value of (

P17P20+5√2P17P19

P18P19+5√2P182

) is equal to ________.

[25 Jul 2021 Shift 1]

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