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2.左-右=∑(2x^2-z^2-y^2)/(y+z) (∑表示循环和)
由于对称,不妨设:x>=y>=z
故1/(x+y)<=1/(x+z)<=1/(y+z)
2x^2-z^2-y^2>=0 2z^2-x^2-y^2<0
(逐次变换分母)
∑(2x^2-z^2-y^2)/(y+z)=(2x^2-z^2-y^2)/(y+z)+(2y^2-z^2-x^2)/(x+z)+(2z^2-x^2-y^2)/(x+y)>=(2x^2-z^2-y^2)/(x+z)+(2y^2-z^2-x^2)/(x+z)+(2z^2-x^2-y^2)/(z+x)=(2x^2-z^2-y^2+2y^2-z^2-x^2+2z^2-x^2-y^2)/(z+x)=0
4.对(1/a-1)而言:1/a-1=(a+b+c)/a-1=(b+c)/a
故原式=(b+c)/a*(a+c)/b*(c+b)*c>=2√bc/a*2√ab/c*2√ac/b=8
由于对称,不妨设:x>=y>=z
故1/(x+y)<=1/(x+z)<=1/(y+z)
2x^2-z^2-y^2>=0 2z^2-x^2-y^2<0
(逐次变换分母)
∑(2x^2-z^2-y^2)/(y+z)=(2x^2-z^2-y^2)/(y+z)+(2y^2-z^2-x^2)/(x+z)+(2z^2-x^2-y^2)/(x+y)>=(2x^2-z^2-y^2)/(x+z)+(2y^2-z^2-x^2)/(x+z)+(2z^2-x^2-y^2)/(z+x)=(2x^2-z^2-y^2+2y^2-z^2-x^2+2z^2-x^2-y^2)/(z+x)=0
4.对(1/a-1)而言:1/a-1=(a+b+c)/a-1=(b+c)/a
故原式=(b+c)/a*(a+c)/b*(c+b)*c>=2√bc/a*2√ab/c*2√ac/b=8
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