x^2/(x+y^2) = x - xy^2/(x+y^2)
原不等式等价于：
xy^2/(x+y^2) + yz^2/(y+z^2) + zx^2/(z+x^2) <= 3/2.
因x+y^2 >= 2sqrt(xy^2), 归结于证明
xsqrt(z) + ysqrt(x) + zsqrt(y) <= 3.
由柯西不等式，
LHS^2 <= (x+y+z)(xz+yx+zy) = 3(xz+yx+zy) <= 9
因xz+yx+zy <= (x+y+z)^2/3.
原不等式等价于：
xy^2/(x+y^2) + yz^2/(y+z^2) + zx^2/(z+x^2) <= 3/2.
因x+y^2 >= 2sqrt(xy^2), 归结于证明
xsqrt(z) + ysqrt(x) + zsqrt(y) <= 3.
由柯西不等式，
LHS^2 <= (x+y+z)(xz+yx+zy) = 3(xz+yx+zy) <= 9
因xz+yx+zy <= (x+y+z)^2/3.
