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  4. Let α, β be two roots of the equation x2+(20)1 / 4 x+(5)1 / 2=0. Then α8+β8 is equal to

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Q. Let $\alpha, \beta$ be two roots of the equation $x^{2}+(20)^{1 / 4} x+(5)^{1 / 2}=0$. Then $\alpha^{8}+\beta^{8}$ is equal to

JEE MainJEE Main 2021Complex Numbers and Quadratic Equations

Solution:

$\left(x^{2}+\sqrt{5}\right)^{2}=\sqrt{20} x^{2}$
$x^{4}=-5 \Rightarrow x^{8}=25$
$\alpha^{8}+\beta^{8}=50$