(x+1/x)^3/2

x+1/x=7
两边平方
x^2+2+1/x^2=49
x^2+1/x^2=47

x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=7*(47-1)=322

[x^(3/2)+x^(-3/2)]^2=x^3+2+1/x^3=322+2=324
因为x^(3/2)=根号(x^3)>=0
同理，x^(-3/2)>=0
所以x^(3/2)+x^(-3/2)>=0

所以x^(3/2)+x^(-3/2)=根号324=18

[x^1/2+x^(-1/2)]^2=x+1/x+2=7+2=9
x^1/2+x^(-1/2)=3.
x^(3/2)+x^(-3/2)=(x^1/2+x^(-1/2))[x-x^1/2*x^(-1/2)+1/x]=3*[7-1]=18