已知x>y>0,xy=1,求证：（x*x+y*y)/(x-y)>=8^(1/2)
证明：
（x*x+y*y)/(x-y)=[（x*x-2xy+y*y)-2xy]/(x-y)
=[（x*x-y*y)-2]/(x-y)
=(x-y))-2/(x-y)
>=2*2^(1/2)
>=8^(1/2)
答：设(3x^3+125y^3)/(x-y)≥t→3x^3+125y^3+yt≥xt. 依xy=1及均值不等式，得 3x^3+125y^3 =x^3+x^3+x^3...详情>>
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