x>y,xy=1.求证:(x*x+y*y)/(x-y)≥2根号2
參考答案:(x^2+y^2)/(x-y)
=[(x-y)^2+2xy]/(x-y)
=x-y+2/(x-y)
≥2根号2
取等号时
x-y=根号2 且xy=1
解得x=(根号6+根号2)/2
y=x=(根号6-根号2)/2
x>y,xy=1.求证:(x*x+y*y)/(x-y)≥2根号2
參考答案:(x^2+y^2)/(x-y)
=[(x-y)^2+2xy]/(x-y)
=x-y+2/(x-y)
≥2根号2
取等号时
x-y=根号2 且xy=1
解得x=(根号6+根号2)/2
y=x=(根号6-根号2)/2