已知x²-5x-1999=0,求代数式(x-2)³-(x-1)²+1/x-2的值已知x²-5x-1999=0,²²求代数式(x-2)³-(x-1)²+1的值 ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄x-2
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![已知x²-5x-1999=0,求代数式(x-2)³-(x-1)²+1/x-2的值已知x²-5x-1999=0,²²求代数式(x-2)³-(x-1)²+1的值 ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄x-2](/uploads/image/z/1619914-58-4.jpg?t=%E5%B7%B2%E7%9F%A5x%26sup2%3B-5x-1999%3D0%2C%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F%EF%BC%88x-2%EF%BC%89%26sup3%3B-%EF%BC%88x-1%29%26sup2%3B%2B1%2Fx-2%E7%9A%84%E5%80%BC%E5%B7%B2%E7%9F%A5x%26sup2%3B-5x-1999%3D0%2C%26sup2%3B%26sup2%3B%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F%28x-2%29%26sup3%3B-%EF%BC%88x-1%29%26sup2%3B%2B1%E7%9A%84%E5%80%BC%EF%BF%A3%EF%BF%A3%EF%BF%A3%EF%BF%A3%EF%BF%A3%EF%BF%A3%EF%BF%A3%EF%BF%A3%EF%BF%A3%EF%BF%A3x-2)
已知x²-5x-1999=0,求代数式(x-2)³-(x-1)²+1/x-2的值已知x²-5x-1999=0,²²求代数式(x-2)³-(x-1)²+1的值 ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄x-2
已知x²-5x-1999=0,求代数式(x-2)³-(x-1)²+1/x-2的值
已知x²-5x-1999=0,²²求代数式(x-2)³-(x-1)²+1的值
 ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄
x-2
已知x²-5x-1999=0,求代数式(x-2)³-(x-1)²+1/x-2的值已知x²-5x-1999=0,²²求代数式(x-2)³-(x-1)²+1的值 ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄x-2
∵x²-5x-1999=0
∴x^2-5x=1999
[(x-2)³-(x-1)²+1]/(x-2)
=[(x-2)³+1-(x-1)²]/(x-2)
={(x-2+1)[(x-2)^2-(x-2)+1]-(x-1)^2}/(x-2)
=[(x-1)(x^2-5x+7)-(x-1)^2]/(x-2)
=(x-1)(x-2)(x-4)/(x-2)
=(x-1)(x-4)
=x^2-5x+4
=1999+4
=2003