Question

已知X平方—5 X—2002=0,则代数式(x—2)立方—(x—1)平方+1除以x—2的值是( )

Answer 1

由已知x^2-5x-2002=0整理得：x^2-5x=2002,则有

[(x-2)^3-(x-1)^2+1]/(x-2)

=[(x-2)^3-(x^2-2x+1)+1]/(x-2)

=[(x-2)^3-x^2+2x]/(x-2)

=[(x-2)^3-x(x-2)]/(x-2)

=(x-2)×[(x-2)^2-x]/(x-2)

=(x-2)^2-x

=x^2-4x+4-x

=x^2-5x+4

=2002+4

=2006

选A