Câu hỏi của Măm Măm

Question

Tìm số tự nhiên x thỏa

$A^2_{x-2}+C^{x-2}_x=101$

Nguyễn Việt Lâm · Accepted Answer

ĐK: $x\ge4$

$\dfrac{\left(x-2\right)!}{\left(x-4\right)!}+\dfrac{x!}{\left(x-2\right)!.2!}=101$

$\Leftrightarrow\left(x-2\right)\left(x-3\right)+\dfrac{x\left(x-1\right)}{2}=101$

$\Leftrightarrow3x^2-11x-190=0$

$\Rightarrow x=10$

Câu trả lời:

ĐK: $x\ge4$

$\dfrac{\left(x-2\right)!}{\left(x-4\right)!}+\dfrac{x!}{\left(x-2\right)!.2!}=101$

$\Leftrightarrow\left(x-2\right)\left(x-3\right)+\dfrac{x\left(x-1\right)}{2}=101$

$\Leftrightarrow3x^2-11x-190=0$

$\Rightarrow x=10$