问题描述: 已知X^2-5X-1991=0 则[(X-2)^4+(X-1)^2-1] / (X-1)(X-2) 的值为 1个回答 分类:数学 2014-10-31 问题解答: 我来补答 [(X-2)^4+(X-1)^2-1] / (X-1)(X-2)={(X-2)^4+[(X-2)+1]^2-1}/(X-1)(X-2)=[(X-2)^4+(X-2)^2+2*(X-2)+1-1]/(X-1)(X-2)=[(X-2)^3+(X-2)+2]/(X-1)=[(X-2)^3+X]/(X-1)={[(X-1)-1]^3+X}/(X-1)=[(X-1)^3-3*(X-1)^2+3*(X-1)-1+X]/(X-1)=(X-1)^2-3(X-1)+2=[(X-1)-1][(X-1)-2]=(X-2)(X-3)=X^2-5X+6已知X^2-5X-1991=0 即:X^2-5X=1991∴[(X-2)^4+(X-1)^2-1] / (X-1)(X-2)=X^2-5X+6=1991+6=1997 展开全文阅读