Question

ache o  valor de 'N" arranjo n; 2= 72. Qual alternativa corresponde:
a)8
b)-8
c)9
d)-9
e)10

Answer 1

ta dificil essa mais eu vou ver se acho a solucao

Answer 2

Olá Glaucia,

use como base o conceito de arranjo simples:

$A_{n,p}= \dfrac{n!}{(n-p)!}\\\\ A_{n,2}=72\\\\ \dfrac{n!}{(n-2)!}=72\\\\\\ \dfrac{n(n-1)(n-2)!}{(n-2)!}=72\\\\\\ \dfrac{n(n-1)(\not n-2)}{(\not n-2)}=72\\\\\\ n(n-1)=72\\ n^2-n=72\\ n^2-n-72=0$

$\Delta=(-1)^2-4*1*(-72)\\ \Delta=1+288\\ \Delta=289\\\\ n= \dfrac{-(-1)\pm \sqrt{289} }{2*1}= \dfrac{1\pm17}{2}\begin{cases}n'= \dfrac{1-17}{2}= \dfrac{-16}{~~2}=-8\notin \mathbb{N}\\\\ n''= \dfrac{1+17}{2}= \dfrac{18}{2} =9 \end{cases}$

Portanto, o valor de N é 9, alternativa C .

Tenha ótimos estudos =))