已知X^2-5X-1991=0,则代数式[(X-2)^4+(X-1)^2-1]/(x-2)(的值

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已知X^2-5X-1991=0,则代数式[(X-2)^4+(X-1)^2-1]/(x-2)(的值

已知X^2-5X-1991=0,则代数式[(X-2)^4+(X-1)^2-1]/(x-2)(的值
已知X^2-5X-1991=0,则代数式[(X-2)^4+(X-1)^2-1]/(x-2)(的值

已知X^2-5X-1991=0,则代数式[(X-2)^4+(X-1)^2-1]/(x-2)(的值
∵X^2-5X-1991=0
∴(x-2)²=x+1995,x²=5x+1991,x=﹙5±√7989﹚/2
∴[(X-2)^4+(X-1)^2-1]/(x-2)
=[(X-2)^4+x(x-2)]/(x-2)
=(x-2)^3+x
=(x+1995)x+x
=x²+1996x
=5x+1991+1996x
=2001x+1991=2001×﹙5±√7989﹚/2+1991=13987/2±2001/2√7989