Question

Добрый вечер! помогите пожалуйста)

Answer 1

$C_x^2 = C_x^3\\\frac{x!}{(x-2)!2!} =\frac{x!}{(x-3)!3!} |:x!\\\frac{1}{2(x-2)!} =\frac{1}{6(x-3)!}\\2(x-2)!=6(x-3)! |:2\\(x-2)!=3(x-3)!\\(x-2)!-3(x-3)!=0\\(x-2)(x-3)!-3(x-3)!=0\\(x-3)!(x-2-3)=0\\(x-3)!=0 => x\in\emptyset\\x-5=0 => x=5$

Ответ: $x=5$

Answer 2

Ответ:

$\boxed{\ C_{n}^{k}=\dfrac{n\cdot (n-1)\cdot ...\cdot (n-k+1)}{k!}\ }\\\\\\\\C_{x}^2=C_{x}^3\ \ ,\ \ \ \ x\in N\ ,\ x\geq 3\\\\\dfrac{x\cdot (x-1)}{2!}=\dfrac{x(x-1)(x-2)}{3!}\\\\3!\cdot x\cdot (x-1)=2!\cdot x(x-1)(x-2)\\\\3!\cdot x\cdot (x-1)-2!\cdot x(x-1)(x-2)=0\\\\2!\cdot 3\cdot x\cdot (x-1)-2!\cdot x(x-1)(x-2)=0\\\\2!\cdot x\cdot (x-1)\cdot \Big(3-(x-2)\Big)=0\\\\2!\cdot x\cdot (x-1)\cdot (5-x)=0\\\\x_1=0<3\ ,\ \ x_2=1<3\ ,\ \ x_3=5\\\\Otvet:\ x=5\ .$