Question

Tìm số tự nhiên x thỏa

\(4C^4_{x-1}-4C^3_{x-1}< 5A^2_{x-2}\)

Answer 1

Điều kiện: \(x\ge5\)

\(\dfrac{4\left(x-1\right)!}{4!.\left(x-5\right)!}-\dfrac{4\left(x-1\right)!}{3!\left(x-4\right)!}< \dfrac{5\left(x-2\right)!}{\left(x-4\right)!}\)

\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x-4\right)}{6}-\dfrac{2\left(x-1\right)}{3}< 5\)

\(\Leftrightarrow x^2-9x-22< 0\)

\(\Rightarrow-2< x< 11\)

\(\Rightarrow x=\left\{5;6;7;8;9;10\right\}\)