已知x²-5x-1997=0,则代数式[(x-2)^3-(x-1)²+1]/(x-2) 的值是
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![已知x²-5x-1997=0,则代数式[(x-2)^3-(x-1)²+1]/(x-2) 的值是](/uploads/image/z/1671245-53-5.jpg?t=%E5%B7%B2%E7%9F%A5x%26%23178%3B-5x-1997%3D0%2C%E5%88%99%E4%BB%A3%E6%95%B0%E5%BC%8F%5B%EF%BC%88x-2%EF%BC%89%5E3-%EF%BC%88x-1%EF%BC%89%26%23178%3B%2B1%5D%2F%EF%BC%88x-2%EF%BC%89+%E7%9A%84%E5%80%BC%E6%98%AF)
已知x²-5x-1997=0,则代数式[(x-2)^3-(x-1)²+1]/(x-2) 的值是
已知x²-5x-1997=0,则代数式[(x-2)^3-(x-1)²+1]/(x-2) 的值是
已知x²-5x-1997=0,则代数式[(x-2)^3-(x-1)²+1]/(x-2) 的值是
∵x²-5x-1997=0
∴x²-5x=1997
[(x-2)^3-(x-1)²+1]/(x-2)
=(x³-6x²+12x-8-x²+2x-1+1)/(x-2)
=(x³-7x²+14x-8)/(x-2)
=(x³-8)-(7x²-14x)/(x-2)
=[(x-2)(x²+2x+4)-7x(x-2)]/(x-2)
=(x-2)(x²+2x-7x+4)/(x-2)
=x²-5x+4
=1997+4
=2001