已知x²-5x-2006=0,求代数式((x-2)^3-(x-1)²+1)/(x-2)的值.

已知x²-5x-2006=0,求代数式((x-2)^3-(x-1)²+1)/(x-2)的值.
已知x²-5x-2006=0,求代数式((x-2)^3-(x-1)²+1)/(x-2)的值.

已知x²-5x-2006=0,求代数式((x-2)^3-(x-1)²+1)/(x-2)的值.
由x²-5x-2006=0知x²-5x=2006
((x-2)^3-(x-1)²+1)/(x-2)=（x-2）^2-(x-1)^2/(x-2)+1/(x-2)
=（x-2）^2-(x^2-2x)/(x-2)
=x^2-5x+4
=2006+4
=2010

((x-2)^3 - (x-1)^2 + 1) / (x-2)
= ((x-2)^3 - (x-2)^2 - 2x + 3 + 1) / (x-2)
= ((x-2)^3 - (x-2)^2 - 2(x-2)) / (x-2)
= (x-2)^2 - (x-2) - 2
= (x-4)(x-1)
= x^2 - 5x + 4
= 2010

由x²-5x-2006=0知x²-5x=2006
((x-2)^3-(x-1)²+1)/(x-2)=（x-2）^2-(x-1)^2/(x-2)+1/(x-2)
=（x-2）^2-(x^2-2x)/(x-2)
=x^2-5x+4
=2006+4
=2010