第1个回答 2010-07-20
【注:因y²-z²=(y²-x²)+(x²-z²),故(y²-z²)/(z+x)=(y²-x²)/(z+x)+(x²-z²)/(z+x)】证明:易知,该式为对称式。不妨设z≥x≥y>0.w=(z²-x²)/(x+y)+(x²-y²)/(y+z)+(y²-z²)/(z+x)=(z²-x²)/(x+y)+(x²-y²)/(y+z)-(x²-y²)/(z+x)-(z²-x²)/(z+x)=(z²-x²)[1/(x+y)-1/(z+x)]+(x²-y²)[1/(y+z)-1/(z+x)]=(z²-x²)(z-x)/[(x+y)(z+x)]+(x²-y²)(x-y)/[(y+z)(z+x)].由z≥x≥y>0易知,w=(z²-x²)(z-x)/[(x+y)(z+x)]+(x²-y²)(x-y)/[(y+z)(z+x)]≥0,等号仅当x=y=z>0时取得。