设x>1,y>0,若x^y+x^-y=2根号2,则x^y-x^-y等于

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x^y+x^-y=2根号2===>(x^y+x^-y)^2=8===>x^2y+x^-2y+2=8===>x^2y+x^-2y=6
(x^y-x^-y)^2=x^2y+x^-2y-2=6-2=4==>x^y-x^-y=2
(a^1/2-b^1/2)/(a^1/2+b^1/2)+(a^1/2+b^1/2)/(a^1/2-b^1/2)=[(a^1/2-b^1/2)^2+(a^1/2+b^1/2)^2]/(a^1/2-b^1/2)(a^1/2+b^1/2)=2(a+b)/(a-b)