一道高中不等式证明题

由柯西不等式：[(y+2z)+(z+2x)+(x+2y)][x^2/(y+2z)+y^2/(z+2x)+z^2/(x+2y)]>=(x+y+z)^2=1且有(y+2z)+(z+2x)+(x+2y)=3(x+y+z)=3所以x^2/(y+2z)+y^2/(z+2x)+z^2/(x+2y)>=1/3证毕.注：本题为2009年浙江省高考数学自选模...