x的负1次方+x=3,求x的平方-x的负2次方和x的二分之三次方+x的负的二分之三次方

x+x^-1=3
两边取平方得：
x^2+x^-2+2=9
x^2+x^-2=7
x^2+x^-2-2=5
(x-x^-1)²=5
x-x^-1=±根号5
x^2-x^-2=(x+x^-1)(x-x^-1)
=±3根号5
2.
x^3/2-x^-3/2
=(X^1/2-X^-1/2)(X+1+1/X)
=4(X^1/2-X^-1/2)
(X^1/2-X^-1/2)^2=X+1/X-2=1
∴X^1/2-X^(-1/2)=±1,
∴原式=±4.