x>0，y>0，且xy＝1，求(x²+y²)/(x-y)的范围
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(1)当x>y时
(x²＋y²﹚／﹙x-y)
=[(x-y)^2+2xy]/(x-y)
=(x-y)+2xy/(x-y)
≥2√[2(x-y)*2xy/(x-y)]=4
则有(x²＋y²﹚／﹙x-y﹚≥4
(2)当0<x<y时
x-y<0
(x²＋y²﹚／﹙x-y)
=[(x-y)^2+2xy]/(x-y)
=-[(y-x)+2xy/(y-x)]
(x²＋y²﹚／﹙x-y)≤-2√[2(y-x)*2xy/(y-x)]=4
x-y<0
则有(x²＋y²﹚／﹙x-y﹚<0
故 (x²+y²)/(x-y)<0或(x²+y²)/(x-y)≥4
(x²＋y²﹚／﹙x-y)
=[(x-y)^2+2xy]/(x-y)
=(x-y)+2xy/(x-y)
≥2√[2(x-y)*2xy/(x-y)]=4
则有(x²＋y²﹚／﹙x-y﹚≥4
(2)当0<x<y时
x-y<0
(x²＋y²﹚／﹙x-y)
=[(x-y)^2+2xy]/(x-y)
=-[(y-x)+2xy/(y-x)]
(x²＋y²﹚／﹙x-y)≤-2√[2(y-x)*2xy/(y-x)]=4
x-y<0
则有(x²＋y²﹚／﹙x-y﹚<0
故 (x²+y²)/(x-y)<0或(x²+y²)/(x-y)≥4
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