Question

Помогите решить уравнение с факториалами. Пожалуйста, срочно((

Answer 1

$\left \{ {{\frac{x!}{(x-y)!}=10\cdot \frac{x!}{(x-(y-1))!}\, } \atop {3\cdot \frac{x!}{y!(x-y)!}=5\cdot \frac{x!}{(y-1)!(x-(y-1))!}}} \right.\\\\a)\; \; \frac{x!}{(x-y)!}=10\cdot \frac{x!}{(x-(y-1))!}\; \; \to \; \; \frac{1}{(x-y)!}=\frac{10}{(x-(y-1))!}\; \; ,\\\\1=\frac{10\cdot (x-y)!}{(x-y+1)!}\; \; ,\; \; 1=\frac{10}{x-y+1}\; \; ,\; \; x-y+1=10\\\\b)\; \; 3\cdot \frac{x!}{y!(x-y)!}=5\cdot \frac{x!}{(y-1)!(x-(y-1))!}\; \; \to \; \; \frac{3}{y!(x-y)!} =\frac{5}{(y-1)!(x-y+1)!}$

$\frac{3}{5}=\frac{y!(x-y)!}{(y-1)!(x-y+1)!} \; ,\; \; \frac{3}{5}=\frac{y}{x-y+1}\; ,\; \; 5y=3(x-y+1)\; ,\\ \\5y=3\cdot 10\; \; \to \; \; y=6\\\\x-y+1=10\; \; \to \; \; x=10+y-1=10+6-1=15\\\\Otvet:\; \; x=15\; ,\; y=6.\\\\\\\star \; \; y!=(y-1)!\, \cdot y\; \; \star \\\\\star \; \; (x-y+1)!=(x-y)!\, \cdot (x-y+1)\; \; \star$