Question

计算根号下2001×2002×2003×2004＋1 请迅速

Answer 1

设x=2002

2001*2002*2003*2004+1

=(x-1)x(x+1)(x+2)+1

=(x^2+x-2)(x^2+x)+1

=(x^2+x-1)^2

√2001×2002×2003×2004＋1

=√（2002^2+2000-1)^2

=2002^2+2000-1

=4010003