Question

求根号2001*2002*2003*2004+1-(没有根号)2002^2的值

Answer 1

设2001=a

则

2001*2002*2003*2004+1

a(a+1)(a+2)(a+3)+1

=[a(a+3)][(a+1)(a+2)]+1

=(a^2+3a)(a^2+3a+2)+1

=(a^2+3a)^2+2(a^2+3a)+1

==(a^2+3a+1)^2

所以

原式=a²+3a+1+-a²-2a-1

=a

=2001