已知x+x^-1=3 , 则x^2 - x^-2 = ？？？

由条件可得:
(x+1/x)^2=9
展开得x^2+2+1/x^2=9
可得x^2-2+1/x^2=5
即(x-1/x)^2=5
开方得x-1/x=正负根5
所以所求式=(x+1/x)*(x-1/x)=3*正负根5=正负3根5

X^2-X^-2
=(X+X^-1)(X-X^-1)=(X+1/X)(X-1/X)
已知X+X^-1=3
所以只要求X-X^-1等于多少就行了.
X+X^-1=3两边平方得
(X+X^-1)^2
=x^2+2+1/x^2
=x^2-2+1/x^2=5
(x-1/x)^2=5
得x-1/x=-5或者5
所以X^2-X^-2
=(X+X^-1)(X-X^-1)
=(X+1/X)(X-1/X)
=3*(-5)或者3*5
=-15或者15

(x+x^-1)^2=x^2+2*x*x^-1+x^-2=3^2=9
即x^2+x^-2=9-2=7