Question

√1999*2000*2001*2002+1怎么做?

Answer 1

方法如果因式分解等变形题的数字较大,可采用换元法,把大数字换成字母

设1999=a,则2000=(a+1).

所以原式=根号[a(a+1)(a+2)(a+3)+1]

=根号{[a(a+3)][(a+1)(a+2)]+1}

=根号{[a^2+3a][a^2+3a+2]+1}

=根号{[a^2+3a+1]^2-1+1}

=根号{[a^2+3a+1]^2}

=a^2+3a+1

=(a+1)^2+a

=(1999+1)^2+1999

=4001999