Aₐᵇ = a!/(a - b)!
Cₐᵇ = a!/b!(a - b)!
a! = 1*2*...*(a-1)*a
12Aₓ₊₃ˣ⁻¹ = 55Aₓ₊₁²
x>2
12(x+3)!/(x - 1)!(x + 3 - x + 1)! = 55(x + 1)!/(x - 1)!
12(x+3)!/(x - 1)!*4! = 55(x + 1)!/(x - 1)!
4! = 1*2*3*4 = 24
(x + 3)(x + 2)(x + 1)x = 110(x + 1)x
(x + 1)x*[(x + 3)(x + 2) - 110] = 0
x + 1 = 0 x = -1 нет
x = 0 нет
(x + 2)(x + 3) = 110
x² + 5x + 6 - 110 = 0
x² + 5x - 104 = 0
D = 25 + 4*104 = 441 = 21²
x12 = (-5 +- 21)/2 = -13 8
x = -13 нет < 2
x = 8 да > 2
ответ 8
Aₐᵇ = a!/(a - b)!
Cₐᵇ = a!/b!(a - b)!
a! = 1*2*...*(a-1)*a
12Aₓ₊₃ˣ⁻¹ = 55Aₓ₊₁²
x>2
12(x+3)!/(x - 1)!(x + 3 - x + 1)! = 55(x + 1)!/(x - 1)!
12(x+3)!/(x - 1)!*4! = 55(x + 1)!/(x - 1)!
4! = 1*2*3*4 = 24
(x + 3)(x + 2)(x + 1)x = 110(x + 1)x
(x + 1)x*[(x + 3)(x + 2) - 110] = 0
x + 1 = 0 x = -1 нет
x = 0 нет
(x + 2)(x + 3) = 110
x² + 5x + 6 - 110 = 0
x² + 5x - 104 = 0
D = 25 + 4*104 = 441 = 21²
x12 = (-5 +- 21)/2 = -13 8
x = -13 нет < 2
x = 8 да > 2
ответ 8