Question

2) Resolva as equações: a) Cx,2 = 10 b) C x,2 = 15. c) C n,2 = 6 d) C n,4 = 4 C n,3

Answer 1

a) Cx,2 = 10

x(x-1)/2 = 10

x²-x -20= 0

(x-5).(x+4)=0

x=5 x=-4. ===> s: x=5

b) C x,2 = 15.

x(x-1)/2=15

x² -x -30=0

(x-6). (x+5)=0

x=6. x=-5 ==> s: x=6

c) C n,2 = 6

n(n-1)/2 = 6

n²- n -12 = 0

(n-4). (n+3)= 0

n=4. n=-3 ==> s: n=4

d) C n,4 = 4 C n,3

n(n-1)(n-2)(n-3)/4.3! = n(n-1)(n-2)/3!

(n-3)/4 = 1

n-3= 4

n=7