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已知方程x+1/x=a+1/a的两根分别为a,1/a,则方程x+1/(x-1)=a+1/(a-1)的根是?
题目详情
已知方程x+1/x=a+1/a的两根分别为a,1/a,则方程x+1/(x-1)=a+1/(a-1)的根是?
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答案和解析
x+1/(x-1)=a+1/(a-1)
(x-1)+1/(x-1)=(a-1)+1/(a-1)
因为方程x+1/x=a+1/a的两根分别为a,1/a
所以x-1=a-1或x-1=1/(a-1)
x=a或a/(a-1)
(x-1)+1/(x-1)=(a-1)+1/(a-1)
因为方程x+1/x=a+1/a的两根分别为a,1/a
所以x-1=a-1或x-1=1/(a-1)
x=a或a/(a-1)
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