x^8 +ax^4 +1=0 a=? is x_1 +x_2 +x_3 +x


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Question Number 161521 by vvvv last updated on 19/Dec/21

$x^{8} + {ax}^{4} + 1 = 0$ $a = ?$ $i s x_{1} + x_{2} + x_{3} + x_{4} = ?$
Commented by mr W last updated on 19/Dec/21

$t h o u g h y o u u s e d t w o t i m e s t h e q u e s t i o n$ $m a r k, b u t y o u {d i d n}^{'} t p u t a c l e a r$ $q u e s t i o n . w h a t i s y o u r e x a c t q u e s t i o n ?$
Commented by Tyller last updated on 19/Dec/21

${(x^{4})}^{2} + {a x}^{4} + 1 = 0$ ${(x^{4} + \frac{a}{2})}^{2} = \frac{a^{2} - 4}{4}$ $x = \pm \sqrt[4]{- \frac{a}{2} \pm \sqrt{\frac{a^{2} - 4}{4}} .}$ $a \in [0, \sqrt{2}]$ $x_{1} + x_{2} + x_{3} + x_{4} = 0$
Commented by mr W last updated on 19/Dec/21

$i t i s n o t s t a t e d t h a t x \in R . s o a c a n b e$ $a n y v a l u e a n d t h e r e a r e g e n e r a l l y 8$ $r o o t s .$ $t h a t i s w h y i s a i d t h e q u e s t i o n i s n o t$ $c l e a r .$
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