Let α, β be the roots of the quadratic equation x²+√(6) x+3=0. Then (α²³+β²³+α¹⁴+β¹⁴)/(α¹⁵+β¹⁵+α¹⁰+β¹⁰) is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 12 Apr, Morning shift · Q5163

JEE Main 202312 Apr, Morning shiftMathematicsHardComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha, \beta

be the roots of the quadratic equation

x^{2}+\sqrt{6} x+3=0

. Then

\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}

is equal to :

JEE Main 2023 · 12 Apr, Morning shift · Q5163

JEE Main 202312 Apr, Morning shiftMathematicsHardComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha, \beta

be the roots of the quadratic equation

x^{2}+\sqrt{6} x+3=0

. Then

\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}

is equal to :