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Question Number 207730 by mr W last updated on 24/May/24

Commented by mr W last updated on 24/May/24

$i s t h i s p o s s i b l e ?$
Commented by efronzo1 last updated on 25/May/24

$i think, no sir$
Commented by mr W last updated on 25/May/24

$i b e l i e v e i t i s p o s s i b l e . r e a s o n :$ $x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + . . . + x_{2023}^{2} = 125$ $i s a s p h e r e i n a 2023 - d i m e n s i o n a l$ $s p a c e w i t h r a d i u s \sqrt{125} .$ $x_{1} + x_{2} + x_{3} + . . . + x_{2023} = 25$ $i s a p l a n e i n t h i s 2023 - d i m e n s i o n a l$ $s p a c e .$ $w e c a n s e e t h a t t h e p l a n e a n d$ $t h e s p h e r e i n t e r s e c t e a c h o t h e r .$ $t h e i n t e r s e c t i o n i s a r i n g i n t h a t$ $s p a c e . a t l e a s t o n e p o i n t o n t h i s r i n g$ $d e l i v e r s t h e m a x i m u m v a l u e f o r$ $x_{1}^{3} + x_{2}^{3} + x_{3}^{3} + . . . + x_{2023}^{3} a n d a t l e a s t o n e$ $p o i n t d e l i v e r s t h e m i n i m u m v a l u e .$
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