Question

ПОМОГИТЕ!!! 85 БАЛОВ
Задания по алгебре-комбинаторике

Answer 1

$\displaystyle A^{x-1}_{x+1}+2P_{x-1}=\frac{30}{7}P_{x}\\\\\frac{(x+1)!}{(x+1-x+1)!}+2(x-1)!=\frac{30}{7}x!\\\\\frac{(x+1)!}{2!}+2(x-1)!=\frac{30}{7}x!\\\\7(x+1)!+28(x-1)!-60x!=0\\\\(x-1)!*(7*x*(x+1)+28-60x)=0\\\\(x-1)!*(7x^2+7x+28-60x)=0\\\\(x-1)!\neq 0; 7x^2-53x+28=0\\\\D=2025\\\\x_{1.2}=\frac{53 \pm 45}{14}\\\\ x_1=7; x_2=\frac{4}{7}$

т.к. x∈N

то х= 7