Question

10 pontos quem responder
Número Binomial
(n)
(p)

(x)+(x)=35
(2) (3)
(resposta:x=6)

Answer 1

Relação de Stifel
$\left(\begin{array}{ccc}n\\p\\\end{array}\right)+ \left(\begin{array}{ccc}n\\p+1\\\end{array}\right) = \left(\begin{array}{ccc}n+1\\p+1\\\end{array}\right) \\ \\ \left(\begin{array}{ccc}x\\2\\\end{array}\right) + \left(\begin{array}{ccc}x\\3\\\end{array}\right)=35 \\ \\ \left(\begin{array}{ccc}x+1\\3\\\end{array}\right) =35 \\ \\ \frac{(x+1)!}{3!(x+1-3)!} =35 \\ \\ \frac{(x+1)!}{6(x-2)!} =35 \\ \\ \frac{(x+1)x(x-1)(x-2)!}{(x-2)!} =6.35 \\ \\ (x-1)x(x+1))=5.6.7$
Como x é número natural, podemos fazer:
x - 1= 5 => x= 6 ou x = 6  ou x + 1 = 7=> x = 6
Resp. x = 6