Question

Com base no estudo da combinação, resolvendo a equação Cx, 2 = 21, encontramos:

a) x = -6 ou x = 7
b) x = -6
c) x = 21
d) x = 13
e) x = 7

Answer 1

Cx, 2 = 21

x.(x-1)/2! = 21

x²-x/2 = 21

x² -x -42 = 0

∆= 1 +168 = 169 => √∆=13

x = -b+√∆/2a = 1+13/2 = 14/2 = 7 ✓

Answer 2

OI...

$(\frac{n}{k}~)~=~\frac{n!}{k!~.~(n-k)!}\\   \\x!/2!~.~(x-2)! = 21\\\\x!=x.(x-1).(x-2)!\\\\logo:\\\\x.(x-1).(x-2)!/2!.(x-2)!=21\\\\x.(x-1)/2!=21\\\\x.(x-1)=-42\\\\x²-x-42=0\\\\a=1; b= -1; c= 42\\\\Calculando~delta$

Δ = b² - 4.a.c

Δ = -1² - 4.1.- 42

Δ = 1 + 168

Δ = 169

Aplicando Bhaskara

x = - b ±√Δ/2.a

x' = - ( -1 ± √169)/2.1

x' = 1  ± 13/2

x' = 14/2

x' = 7

x" = - (- 1 - 13)/2.1

x" = 1 - 13/2

x" = - 12/2

x" = - 6

x ∈ N = x = 7

Resposta: letra e = x = 7

Bons estudos.