Question

1. Rezolvaţi ecuaţiile:
a) C³n=2n

Answer 1

Răspuns:

n!/3! •(n-3)!=2n. "!" = factoriale

(n-3)! • (n-2) •(n-1) •n/ 6•(n-3)! =2n

simplificare (n-3)!

(n-2)(n-1)n/6=2n | :n

n²-3n+2/6=2

n²-3n+2=12

n²-3n-10=0

delta= 9-4•1• (-10) = 49

n= 3+7/2=5

n= 3-7/2= -2