已知x²-5x-2006=0,求代数式(x-2)³-(x-1)²+1/x-2的值
问题描述:
已知x²-5x-2006=0,求代数式(x-2)³-(x-1)²+1/x-2的值
答
x^2-5x-2006=0x^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