Question

X+X的负一次方=3,求X的2/3次方-X的2/3次方

Answer 1

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

[x+x^(-1)]^3=x^3+3x+3x^(-1)+x^(-3)=x^3+x^(-3)+9=3^3=27

x^3+x^(-3)=27-9=18

x^(2/3)+x^(-2/3)=根号（18+2）=2*根号5

^表示乘方