Question

Tìm số tự nhiên x thỏa:

\(\dfrac{1}{C^x_4}-\dfrac{1}{C^x_5}=\dfrac{1}{C^x_6}\)

Answer 1

ĐK: \(0\le x\le4\)

\(\dfrac{x!\left(4-x\right)!}{4!}-\dfrac{x!\left(5-x\right)!}{5!}=\dfrac{x!\left(6-x\right)!}{6!}\)

\(\Leftrightarrow1-\dfrac{5-x}{5}=\dfrac{\left(5-x\right)\left(6-x\right)}{30}\)

\(\Leftrightarrow x^2-17x+30=0\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=15\left(loại\right)\end{matrix}\right.\)