已知x^2-5x-1997=0,求代数式[(x-2)(x-2)-(x-1)(x-1)+1]/(x-2)的值...

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已知x^2-5x-1997=0,求代数式[(x-2)(x-2)-(x-1)(x-1)+1]/(x-2)的值...
已知x^2-5x-1997=0,求代数式[(x-2)(x-2)-(x-1)(x-1)+1]/(x-2)的值...

已知x^2-5x-1997=0,求代数式[(x-2)(x-2)-(x-1)(x-1)+1]/(x-2)的值...
[(x-2)(x-2)-(x-1)(x-1)+1]/(x-2)
={[(x-2)+(x-1)][(x-2)-(x-1)]+1}/(x-2)
=[-(2x-3)+1]/(x-2)
=(4-2x)/(x-2)
=-2

[(x-2)(x-2)-(x-1)(x-1)+1]/(x-2)=(4-2x)/(x-2)=-2

x^2-4x=x+1997,x^2-2x=3x+1997 所以:(x-2)(x-2)-(x-1)(x-1)+1]/(x-2) =(x+1997+4-3x-1997)/(x-2)=-2

原式=[x²-4-﹙x²-2x+1﹚+1]/﹙x-2﹚
=﹙x²-4x+4-x²+2x-1+1﹚/﹙x-2﹚
=﹙﹣2x+4﹚/﹙x-2﹚
=﹣2﹙x-2﹚/﹙x-2﹚
=﹣2