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
x^2-5x-2006=0
x^2-5x = 2006
[(x-2)^3-(x-1)^2+1]/(x-2)
=(x-2)^2+[-(x-1)^2+1]/(x-2)
=(x-2)^2+[-x^2+2x-1+1]/(x-2)
=(x^2-4x+4) - x(x-2)/(x-2)
=x^2-4x+4- x
=x^2-5x+4
=2006+4=2010

x²-5x-2006=0
x²-5x = 2006
[(x-2)³-(x-1)²+1]/(x-2)
=(x-2)²+[-(x-1)²+1]/(x-2)
=x²-4x+4- x
=x²-5x+4
=2006+4=2010