please help me to solve this in N A_n ^2 −3C


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Question Number 85322 by mathocean1 last updated on 20/Mar/20

$p l e a s e h e l p m e t o s o l v e t h i s i n N$ $A_{n}^{2} - 3 C_{n}^{n - 2} + n = - 20$
Commented by mr W last updated on 20/Mar/20

$w h a t d o y o u w a n t t o g e t e x a c t l y ?$ $d o y o u w a n t t o g e t A_{n} ? t h i s i s$ $p o s s i b l e : A_{n} = \pm \sqrt{3 C_{n}^{n - 2} - n - 20}$ $o r d o y o u w a n t t o s o l v e f o r n ? t h i s$ $i s n o t p o s s i b l e, b e c a u s e i t i s n o t$ $g i v e n w h a t A_{n} i s .$
Commented by mathocean1 last updated on 20/Mar/20

$A_{n}^{2} = \frac{n!}{(n - 2)!} t h i s i s t h e f o r m u l a t h a t$ $i h a v e .$
Commented by mr W last updated on 20/Mar/20

$w h a t d o y o u m e a n w i t h C_{n}^{n - 2} ?$
Commented by mr W last updated on 20/Mar/20

$f o r c o m b i n a t i o n c a l c u l a t i o n$ $C_{r}^{n} i s d e f i n e d o n l y f o r 0 ⩽ r ⩽ n$ $t h e r e f o r e C_{n}^{n - 2} i s n o t p o s s i b l e!$ $o r d o y o u m e a n {(C_{n})}^{n - 2} ? t h e n y o u$ $m u s t s p e c i f y w h a t i s C_{n} .$
Commented by mr W last updated on 20/Mar/20

$i t h i n k y o u r q u e s t i o n i s n o t c o r r e c t .$ $p l e a s e r e c h e c k!$
Commented by mathocean1 last updated on 20/Mar/20

$I r e c h e c k e d i t s i r . . .$
Commented by mathocean1 last updated on 20/Mar/20

$I t i s l i k e t h i s .$ $I t h i n k t h a t C_{n}^{n - 2} = \frac{n!}{2 \times (n - 2)!}$
Commented by mr W last updated on 20/Mar/20

$y o u w r i t e C_{n}^{n - 2}, b u t y o u m e a n C_{n - 2}^{n} .$
Commented by mr W last updated on 20/Mar/20

$s o y o u r q u e s t i o n i s t o s o l v e n f o r$ $A_{n}^{2} - 3 C_{n - 2}^{n} + n = - 20$ $w i t h A_{n}^{2} = \frac{n!}{(n - 2)!}$ $\frac{n!}{(n - 2)!} - 3 \times \frac{n!}{2! (n - 2)!} + n = - 20$ $\frac{n!}{(n - 2)!} - n = 20$ $n (n - 1) - n = 20$ $n^{2} - 2 n - 20 = 0$ $n = 1 + \sqrt{21} \notin N$ $\Rightarrow n o s o l u t i o n!$ $a g a i n : t h e q u e s t i o n i s w r o n g!$
Commented by mathocean1 last updated on 20/Mar/20

$y e s$
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