[tex]y=\dfrac{3x^2-3xy+3y^2}{3(x^2+xy+y^2)}=\dfrac{x^2+xy+y^2+2(x-y)^2}{3(x^2+xy+y^2)}=\dfrac{1}{3}+\dfrac{2(x-y)^2}{3(x^2+xy+y^2)} \geq \dfrac{1}{3}[/tex]
[tex]y=\dfrac{3(x^2+xy+y^2)-2(x^2+2xy+y^2)}{x^2+xy+y^2}=3-\dfrac{2(x+y)^2}{x^2+xy+y^2} \leq 3[/tex]
C