(x2+y2)/(x-y)=(x2+y2-2xy+2xy)/(x-y)因为xy=1，所以=[(x-y)^2+2]/(x-y)=(x-y)+2/(x-y)因为x>y>0所以(x-y)>0所以有不等式的定理知道（x-y)+2/(x-y)>=2根号下[（x-y)*2/(x-y)]=2根号2而此时（x-y)^2=2符合上面的条件所以(x2+y2)/(x-y)的最小值为2根号2
