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Quadratic Equation and Inequalities question

2021 · 25 Jul · Shift 1 · Q43

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JEE Main
Mathematics
Quadratic Equation and Inequalities
2021 · 25 Jul · Shift 1 · Q43

Quadratic Equation and Inequalities question

2021 · 25 Jul · Shift 1 · Q43

JEE MainMathematicsQuadratic Equation and InequalitiesNumerical+4 / −1

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( {{{{P_{17}}{P_{20}} + 5\sqrt 2 {P_{17}}{P_{19}}} \over {{P_{18}}{P_{19}} + 5\sqrt 2 P_{18}^2}}} \right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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