[评论]数学趣题(55):算式的规律

小小无忧

由题假设:
(X-1)X(X+1)(X+2)+1=Y*Y
=> X*X*X*X + 2X*X*X - X*X - 2X +1 = Y*Y
=> (X*X + X - 1) *  (X*X + X - 1) = Y*Y
所以 Y=(X*X + X - 1) (注意: X 是第二个数)

因此: 2000×2001×2002×2003 + 1 =(2001*2001 + 2001 - 1) 的平方, 即4006001.

ehu1

2000×2001×2002×2003 + 1
=(2001x2001+2000)x(2001x2001+2000)

rule:
(a-1)*a*(a+1)*(a+2)+1
=(a*a+a-1)*(a*a+a-1)

gordonqu

general rule:
  
   x(x+1)(x+2)(x+3)+1=(x*x+3x)(x*x+3x+2)+1
=(x*x+3x)^2+2(x*x+3x)+1=(x*x+3x+1)^2



   2000*2001*2002*2003=(2000*2000+3*2000+1)^2
  =4006001*4006001

lukecheng

(2000x2003+1)(2000x2003+1)