设x>0,y>0若 x^y+x^-y=2√2,则x^y-x^-y等于＿＿＿

设x>0,y>0若 x^y+x^-y=2√2,则x^y-x^-y等于(土2)

x>0,y>0
x^y>0,x^-y>0
x^y+x^-y=2√2
(x^y+x^-y)^2=(2√2)^2
x^2y+2x^y*x^-y+x^-2y=8
x^2y+2+x^-2y=8
x^2y-2+x^-2y=4
x^2y-2x^y*x^-y+x^-2y=4
(x^y-x^-y)^2=4
x^y+x^-y=土2

0

令a=x^y，b=x^-y，已知ab=1，a+b=2√2,
a-b=√(（a+b）^2-4ab)
=√(8-4)
=√4
=2或者-2