Question

resolva a equaçao Cn,2=Cn,3

Answer 1

Olá, Jullya.

 

$<var>C_{n,2}=C_{n,3} \Rightarrow \\\\ \binom n 2=\binom n 3 \Rightarrow \\\\ \frac{n!}{(n-2)!2!}=\frac{n!}{(n-3)!3!} \Rightarrow \\\\ \frac{n!}{(n-2)(n-3)!2!}=\frac{n!}{(n-3)!3\cdot2!} \Rightarrow \\\\ \frac1{(n-2)}\cdot \frac{n!}{(n-3)!2!}=\frac13 \cdot \frac{n!}{(n-3)!2!} \Rightarrow \\\\ \frac1{(n-2)}=\frac13 \Rightarrow \\\\ n-2=3 \Rightarrow \\\\ \boxed{n=5}</var>$