Question

Encontre o valor de n ∈ N, tal que: n!/2!⋅(n−2)!=45.

Answer 1

$\frac{n!}{2! . (n - 2)!} = 45 \\ \frac{n . (n - 1) . (n - 2)!}{2 . (n - 2)!} = 45 \\ \\ \frac{n . (n - 1)}{2} = 45 \\ \\ n^{2} - n = 45 . 2 \\ \\ n^{2} - n - 90 = 0$

Δ = b² - 4ac
Δ = (- 1)² - 4 . 1 . (- 90)
Δ = 1 - 4 . (- 90)
Δ = 1 + 360
Δ = 361

x' = - b + √ Δ / 2a
x' = - (- 1) + √361 / 2 . 1
x' = 1 + 19 / 2
x' = 20 / 2
x' = 10

x" = 1 - 19 / 2
x" = - 18 / 2
x" = - 9