the average of 10 numbers is 5. the sum of their squares is 5000. how large can the largest number among them at most be and how small can the smallest number among them at most be?


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Question Number 180889 by mr W last updated on 18/Nov/22

$t h e a v e r a g e o f 10 n u m b e r s i s 5 . t h e$ $s u m o f t h e i r s q u a r e s i s 5000 . h o w$ $l a r g e c a n t h e l a r g e s t n u m b e r a m o n g$ $t h e m a t m o s t b e a n d h o w s m a l l c a n$ $t h e s m a l l e s t n u m b e r a m o n g t h e m$ $a t m o s t b e ?$
Commented by mr W last updated on 20/Nov/22

$t h e l a r g e s t n u m b e r c a n a t m o s t b e$ $5 + 5 \sqrt{11}$ $t h e s m a l l e s t n u m b e r c a n a t m o s t b e$ $5 - 5 \sqrt{11}$
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