Question

Tentukan nilai n jika C ( n+2 , 4 ) = 6C ( n , 5 )

Answer 1

Berarti :

(n+2)!/(n+2-4)!.4! = 6(n!/(n-5)!.5!)

(n+2)!/(n-2)!.4! = 6(n!/(n-5)!.5!)

(n-2)!.(n-1) (n) ( n+1) ( n+2) / (n-2)!.24 = 6 ((n-5)!.(n-4) (n-3) (n-2) (n-1) (n) / (n-5)!.120

( n-1) (n) (n+1) (n+2)/ 24 = 6 (n-4) (n-3) (n-2) (n-1) (n) / 120

(n+1) (n+2) / 24 = 6 (n-4) (n-3) (n-2) / 120

24(6(n-4) (n-3) (n-2)) = 120 (n+1) (n+2)

144 ( n-4) (n-3) (n-2) = 120 (n+1) (n+2)

144 (n²-7n+12) (n-2) = 120 (n²+3n+2)

144 (n³-9n²+26n-144) = 120n² +360n + 240

144n³ - 1296n² + 3744n - 20736 = 120n² + 360n + 240

144n³ - 1416n² + 3384n - 20976 = 0

6n³ - 59n² + 141n - 874 = 0

Tinggal cari n nya