Aₙᵇ = a!/(a - b)!

a>b a b  натуральные

a! = 1*2*3*....*(a-1)*a

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Aₓ³ =  1/20 * Aₓ⁴

x>=4

x!/(x - 3)! = 1/20*x!/(x-4)!

x(x-1)(x-2) = 1/20*x(x-1)(x-2)(x-3)

20x(х - 1)(х - 2) = x(x - 1)(x - 2)(x - 3)

20x(х - 1)(х - 2) - x(x - 1)(x - 2)(x - 3) = 0

x(х - 1)(х - 2)[20 - (x - 3)] = 0

x(х - 1)(х - 2)(23 - x) = 0

x1=0   x>3 НЕТ

x2=1   x>3 Нет

x3=3   x>3 Нет

x4 = 23

Ответ   x=23

Verified answer

20(х - 1)(х - 2) = (x - 1)(x - 2)(x - 3);

20(х - 1)(х - 2) - (x - 1)(x - 2)(x - 3) = 0;

(х - 1)(х - 2)(20 - (x - 3)) = 0;

(х - 1)(х - 2)(20 - x + 3) = 0;

(х - 1)(х - 2)(23 - x) = 0;

x₁ = 1; x₂ = 2  - не удовлетворяют уравнение; x₃ = 23.

Ответ: 23.