已知x^1/2-x^-1/2=5,求x-x^-1

已知x^1/2-x^-1/2=5,求x-x^-1

x^1/2-x^-1/2=5
(x^1/2-x^-1/2)²=25
x-2+x^-1=25
x+2+x^-1=29
(x^1/2+x^-1/2)²=29
x^1/2+x^-1/2=±√29

当x^1/2+x^-1/2=√29时
x-x^-1
=(x^1/2-x^-1/2)(x^1/2+x^-1/2)
=5√29

当x^1/2+x^-1/2=-√29时
x-x^-1
=(x^1/2-x^-1/2)(x^1/2+x^-1/2)
=-5√29

√表示根号

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√x-1/√x=5
x-2+1/x=25
x+1/x=27

[x^1/2+x^(-1/2)]^2=[x^1/2-x^(-1/2)]^2+4=25+4=29
因为x^1/2+x^(-1/2)>0
故有x^1/2+x^(-1/2)=根号29
x-x^(-1)=(x^1/2+x^(-1/2))(x^1/2-x^(-1/2))=5根号29