Question

Aranjamente de (n+2) luate câte 2 = 56. Habar nu am cum as putea sa o fac

Answer 1

(n+1)(n+2) = 56
n^2 + 3n - 54 = 0
delta = 9 - 4 x (-54) = 225
n = (-3 + 15)/2 = 6
-9 nu este soluție.

Answer 2

[tex]\it A^2_{n+2} =56 \Rightarrow \dfrac{(n+2)!}{(n+2-2)!} =56 \Rightarrow \dfrac{(n+2)!}{n!} = 56\Rightarrow \\\;\\ \\\;\\ \Rightarrow \dfrac{n!(n+1)(n+2)}{n!}=56 \Rightarrow (n+1)(n+2)=56 \ \ \ \ (1) \\\;\\ \\\;\\ 7\cdot 8 = 56 \ \ \ \ (2) [/tex]

$\it (1), (2) \Rightarrow n+1 = 7 \Rightarrow n = 6.$