Cₓ₊₂ˣ⁻¹ = (x+2)!/(x -1)!(x+2 -x+1)! = (x+2)! / (x -1)!3! = x(x+1)(x+2)/6
Aₓ³ = x!/(x-3)! = (x-2)(x -1)x
само уравнение:
12/7*x(x+1)(x+2)/6 = (x-2)(x -1)x
2x(x+1)(x+2) =7х(х-1)(х-2)
2x(x+1)(x+2) -7х(х-1)(х-2) = 0
х( 2(х² +3х +2) -7(х² -3х +2) ) = 0
х = 0 или 2(х² +3х +2) -7(х² -3х +2) =0
2х² +6х +4 -7х² +21х -14 = 0
-5х² +27х -10= 0
5х² -27х +10 = 0
D = b² -4ac = 729 -200 =
x = (27+23)/10 = 5
x = (27 -23)/10 = 0,4