If a and b are the roots of the equation x²-7 x-1=0, then the value of (a²¹+b²¹+a¹⁷+b¹⁷)/(a¹⁹+b¹⁹) is equal to _ _ _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Morning shift · Q44

JEE Main 202311 Apr, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

a

and

b

are the roots of the equation

x^{2}-7 x-1=0

, then the value of

\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}

is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.