证明:对任意a>1,b>1,有不等式a^2/(b-1)+b^2/(a-1)大于等于8
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证明:对任意a>1,b>1,有不等式a^2/(b-1)+b^2/(a-1)大于等于8
证明:对任意a>1,b>1,有不等式a^2/(b-1)+b^2/(a-1)大于等于8
证明:对任意a>1,b>1,有不等式a^2/(b-1)+b^2/(a-1)大于等于8
设元:设x=a-1
y=b-1
则原不等式等价于:x,y>0
求证:(x+1)^2/y+(y+1)^2/x>=8
而::(x+1)^2/y+(y+1)^2/x>=2√[【(x+1)^2(y+1)^2】/xy]
由于(x+1)^2>=4x
(y+1)^2>=4y
故::(x+1)^2/y+(y+1)^2/x>=2√[【(x+1)^2(y+1)^2】/xy]
>=2√[【4x*4y】/xy]
=8
等号当且仅当:x=y=1时取得
以上