Question

Aranjamente de x-1 luate cate 2 - combinări de x-1 luate cate 2 = 15

Answer 1

(x-1)! / (x-3)! - (x-1)! / 2!(x-3)! = (x-2)(x-1) - (x-2)(x-1) / 2 = (x-2)(x-1) / 2 = 15⇒
x²- x - 2x +2 = 30
x² - 3x -28 = 0
Δ = 9 + 112 = 121
x₁ = (3 + 11)/2 = 7
x₂ = (3 - 11) / 2 = -4

Answer 2

$A^2_{x-1}- C^2_{x-1}=15 \\ DVA:x \geq 1 \\ \frac{(x-1)!}{(x-1-2)!}- \frac{(x-1)!}{2(x-1-2)!}=15 \\ \frac{2(x-3)!(x-2)(x-1)-(x-3)!(x-2)(x-1)}{2(x-3)!}=15 \\ \frac{(x-3)!(x-2)(x-1)}{2(x-3)!}=15 \\ (x-2)(x-1)=30 \\ x^2-3x-28=0 \\ x1=-4 \\ x2=7$
x=7∈DVA