Question

已知x+x^(-1)=3,求下列各值：

Answer 1

1.[x^(1/2)+x^(-1/2)]^2=x+1/x+2=3+2=5

则

x^(1/2)+x^(-1/2)=根号5或-根号5

2.(x+1/x)^2=x^2+1/x^2+2=9

则

x^2+1/x^2=7

3.(x-1/x)^2=(x^2+1/x^2)-2=7-2=5

则

x-1/x=根号5或-根号5

x^2-1/x^2=(x+1/x)(x-1/x)

=3*(根号5)或-3(根号5)