Question

(n-2)!=20*(n-4)!\\\\\\\\\\\\\\\\\\\

Answer 1

.
$(n-2)!=20.(n-4)! [tex] \frac{(n-2)!}{(n-4)!} =20 \\ \\ \frac{(n-2)(n-3)(n-4)}{(n-4)} =20 \\ \\ (n-2)(n-3)=20 \\ \\ n^2-5n+6=20 \\ \\ n^2-5n-14=0$

delta=25+56=81

$n= \frac{5+9}{2} = \frac{14}{2} =7 \\ \\ n"=-2~~n/~~serve$

S={7}

Answer 2

$(n-2)!=20(n-4)!\\\\(n-2)(n-3)(n-4)!=20(n-4)!\\\\(n-2)(n-3)=20\\\\(n-2)(n-3)=5\cdot4\\\\\begin{cases}n-2=5\\n-3=4\end{cases}\\\\\boxed{n=7}$