C² x = х! / (2! * (х - 2)!) = U
ОДЗ: хєN, x>=2
х! = 1*2....*(x-3)*(x-2)*(x-1)*x
(x-2)! = 1*2....*(x-3)*(x-2)
U = (1*2....*(x-3)*(x-2)*(x-1)*x) / (2! * 1*2....*(x-3)*(x-2)) = (x-1)*x / 2! = (x-1)*x / (1*2) = (x-1)*x / 2
(x-1)*x / 2 = 66
(x-1)*x = 66*2
(x-1)*x = 132
x^2 - x = 132
x^2 - x - 132 = 0
Дискриминант:
D = (-1)^2 - 4*1*(-132) = 1 + 528 = 529
√D = 23
Первое неизвестное
x = (-(-1) + 23)/(2*1) = (1+23)/2 = 24/2 = 12
Второе неизвестное
x = (-(-1) - 23)/(2*1) = (1-23)/2 = -22/2 = -11
-11 < 2, поэтому это неизвестное отбрасываем
х = 12