利用柯西不等式
∵x,y,z大于0,x+y+z=1
∴x^2/(y+z)+y^2/(z+x)+z^2/(y+x)
=｛[x/√（y+z)]²+ [ y/√(z+x)]²+[z/√(y+x)]²｝[（√（y+z））²+（√（z+x））²+（√（y+x））²]≥（x+y+z)²
∴x^2/(y+z)+y^2/(z+x)+z^2/(y+x)
≥（x+y+z)²/2（x+y+z)=1/2
当且仅当x=y=z=1/3时等号成立
已知x+y+z=1,x,y,z大于0,求证:x^2/(y+z)+y^2/(z+x)+z^2/(y+x)大于等于1/2
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