已知x^2-5x-2014=0,求(x-2)^3-(x-1)^2+1/x-2的值.
问题描述:
已知x^2-5x-2014=0,求(x-2)^3-(x-1)^2+1/x-2的值.
答
x²-5x-2014=0
x²-5x=2014
是这个吗
[(x-2)³-(x-1)²+1]/(x-2)
=(x-2)²-[(x-1)²-1]/(x-2)
=(x-2)²-[(x-1)-1][(x-1)+1]/(x-2)
=(x-2)²-x(x-2)/(x-2)
=x²-4x+4-x
=x²-5x+4
=2014+4
=2018