Determine o valor de n nas equações :
Anexos:
![](https://pt-static.z-dn.net/files/d77/dd97f433671fa7839e88ae2f4a77287b.jpg)
mayarmj:
embaixo não seria "(n-2)!" ??
Soluções para a tarefa
Respondido por
5
a)![\frac{n!}{(n-2)!} =56 \frac{n!}{(n-2)!} =56](https://tex.z-dn.net/?f=+%5Cfrac%7Bn%21%7D%7B%28n-2%29%21%7D+%3D56)
![\frac{n.(n-1).(n-2)!}{(n-2)!} =56 \frac{n.(n-1).(n-2)!}{(n-2)!} =56](https://tex.z-dn.net/?f=+%5Cfrac%7Bn.%28n-1%29.%28n-2%29%21%7D%7B%28n-2%29%21%7D+%3D56)
![n.(n-1)=56 n.(n-1)=56](https://tex.z-dn.net/?f=n.%28n-1%29%3D56)
![n^{2}-n=56 n^{2}-n=56](https://tex.z-dn.net/?f=+n%5E%7B2%7D-n%3D56)
![n^{2} -n-56=0 n^{2} -n-56=0](https://tex.z-dn.net/?f=+n%5E%7B2%7D+-n-56%3D0)
Δ![= b^{2} -4.a.c = b^{2} -4.a.c](https://tex.z-dn.net/?f=%3D+b%5E%7B2%7D+-4.a.c+)
Δ![1^{2} -4.1.56 1^{2} -4.1.56](https://tex.z-dn.net/?f=+1%5E%7B2%7D+-4.1.56)
Δ![= 1 - 224 = 1 - 224](https://tex.z-dn.net/?f=%3D+1+-+224)
Δ![= -223 = -223](https://tex.z-dn.net/?f=%3D+-223)
Não existe raiz real
b) (n+2)!+(n+1)!=15n!
(n+2)(n+1)n!+(n+1)n!=15n!
(n+2)(n+1)+n+1=15
n²+3n+2+n+1=15
n²+4n-12=0
Δ![= 4^{2} -4.1.(-12) = 4^{2} -4.1.(-12)](https://tex.z-dn.net/?f=%3D++4%5E%7B2%7D+-4.1.%28-12%29)
Δ![= 16 + 48 = 16 + 48](https://tex.z-dn.net/?f=%3D+16+%2B+48)
Δ![= 64 = 64](https://tex.z-dn.net/?f=%3D+64)
x=![\frac{-4+ \sqrt{64} }{1.2} = \frac{-4+8}{2} = \frac{4}{2} =2 \frac{-4+ \sqrt{64} }{1.2} = \frac{-4+8}{2} = \frac{4}{2} =2](https://tex.z-dn.net/?f=+%5Cfrac%7B-4%2B+%5Csqrt%7B64%7D+%7D%7B1.2%7D+%3D++%5Cfrac%7B-4%2B8%7D%7B2%7D+%3D++%5Cfrac%7B4%7D%7B2%7D+%3D2)
x =![\frac{-4-8}{2}= \frac{-12}{2} =-6 \frac{-4-8}{2}= \frac{-12}{2} =-6](https://tex.z-dn.net/?f=+%5Cfrac%7B-4-8%7D%7B2%7D%3D+%5Cfrac%7B-12%7D%7B2%7D+%3D-6+)
Raiz = ( 2 e -6)
Δ
Δ
Δ
Δ
Não existe raiz real
b) (n+2)!+(n+1)!=15n!
(n+2)(n+1)n!+(n+1)n!=15n!
(n+2)(n+1)+n+1=15
n²+3n+2+n+1=15
n²+4n-12=0
Δ
Δ
Δ
x=
x =
Raiz = ( 2 e -6)
Perguntas interessantes