Question

A solução da equação An,2 = 20 é *


5

10

15

20

25

​

Answer 1

Explicação passo-a-passo:

$\sf A_{n,2}=20$

$\sf \dfrac{n!}{(n-2)!}=20$

$\sf \dfrac{n\cdot(n-1)\cdot(n-2)!}{(n-2)!}=20$

$\sf n\cdot(n-1)=20$

$\sf n^2-n=20$

$\sf n^2-n-20=0$

$\sf \Delta=(-1)^2-4\cdot1\cdot(-20)$

$\sf \Delta=1+80$

$\sf \Delta=81$

$\sf n=\dfrac{-(-1)\pm\sqrt{81}}{2\cdot1}=\dfrac{1\pm9}{2}$

$\sf n'=\dfrac{1+9}{2}~\Rightarrow~n'=\dfrac{10}{2}~\Rightarrow~\red{n'=5}$

$\sf n"=\dfrac{1-9}{2}~\Rightarrow~n"=\dfrac{-8}{2}~\Rightarrow~\red{n"=-4}$ (não serve)

Logo, n = 5