x-9-2022x-3-2021-0-x-

Question Number 163163 by mathlove last updated on 04/Jan/22

x^{9} - 2022 x^{3} + \sqrt{2021} = 0

x = {?}

Commented by mr W last updated on 04/Jan/22

w h a t d o y o u w a n t t o s a y w i t h {?} ?

d o y o u j u s t m e a n x = ? ?

Answered by mr W last updated on 04/Jan/22

l e t x^{3} = t

t^{3} - 2022 t + \sqrt{2021} = 0

t = 2 \sqrt{674} \sin (\frac{2 k π}{3} + \frac{1}{3} \sin^{- 1} \frac{1}{1348} \sqrt{\frac{2021}{674}}) (k = 0, 1, 2)

\Rightarrow x = \sqrt[3]{2 \sqrt{674} \sin (\frac{2 k π}{3} + \frac{1}{3} \sin^{- 1} \frac{1}{1348} \sqrt{\frac{2021}{674}})}

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