Question

Комбінаторика. Как можно быстрее

Answer 1

$C_{x+2}^{2}=91\\\\\dfrac{(x+2)!}{2!\cdot (x+2-2)!}=91\\\\\\\dfrac{(x+2)!}{2!\cdot x!}=91\\\\\\\dfrac{x!\cdot (x+1)\cdot(x+2)}{1\cdot 2\cdot x!}=91 \\\\\\\dfrac{(x+1)(x+2)}{2}=91\\\\\\(x+1)(x+2)=182\\\\x^{2}+2x+x+2-182=0\\\\x^{2}+3x-180=0\\\\D=3^{2} -4\cdot (-180)=9+720=729=27^{2}\\\\x_{1} =\frac{-3+27}{2}=12\\\\x_{2}=\frac{-3-27}{2}=-15<0-neyd\\\\Otvet:\boxed{12}$