Question

5*n!/3!(n-3)! = (n+2)!/4!(n-2)!

Решите ! ​

Answer 1

n=3 or n=14

Объяснение:

$5!n!(n-2)!=3!(n+2)!(n-3)!\\20(n-2)=(n+1)(n+2)\\n^2-17n+42=0\\n=3\\n=14$

Answer 2

$\displaystyle \frac{5 \times n!}{3!(n - 3)!} = \frac{(n + 2)!}{4!(n - 2)!}$

$\displaystyle \frac{5n(n - 1)(n - 2)(n - 3)!}{3!(n - 3)!} = \frac{(n + 2)!}{4!(n - 2)!}$

(n-3)! сокращаем:

$\displaystyle \frac{5n(n - 1)(n - 2)}{6} = \frac{(n + 2)(n + 1)n(n - 1)(n - 2)(n - 3)!}{24(n - 2)(n - 3)!}$

(n-2) и (n-3)! сокращаем

$\displaystyle \frac{5n(n - 1)(n - 2)}{6} = \frac{(n + 2)(n + 1)n(n - 1)}{24}$

Решаем уравнение.

ответ:n1=3;n2=14.