设x>1,y>0,若x^y+x^-y=2根号2,则x^y-x^-y等于A根号6 B根号2 C-2 D2若m^3/2+m^-1/2=_数学解答

设x>1,y>0,若x^y+x^-y=2根号2,则x^y-x^-y等于
A根号6 B根号2 C-2 D2
若m^3/2+m^-1/2=4,则(m^3/2-m^-3/2)/(m^1/2-m^-1/2)=?
化简 (a^1/2-b^1/2)/(a^1/2+b^1/2)+(a^1/2+b^1/2)/(a^1/2-b^1/2)=?

人气：351 ℃　时间：2020-04-12 15:02:57

解答

D
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)