Question

解方程：(2n+1)!/(2n-3)!=126n!/(n-3)!

Answer 1

左边约去(2n-3)!,右边约去(n-3)!,得

(2n+1)2n(2n-1)(2n-2)=126n(n-1)(n-2)

两边再约去2n(n-1),得

(2n+1)(2n-1)*2=63(n-2)

即8n^2-2=63n-126

∴8n^2-63n+124=0

解得n=4 ,n=-31/8（舍去）

∴n＝4