Ta co:12=x^{2}+y^{2}+xy=(x+y)^{2}-xy\geq(x+y)^{2}-\frac{(x+y)^{2}}{4}=\frac{3(x+y)^{2}}{4}\Rightarrow \left| {x+y} \right|\leq 4$\Rightarrow S=x+y\geq -4Dau "=" xay ra \Leftrightarrow $x=y=-2
Ta co:
12=x^{2}+y^{2}+xy=(x+y)^{2}-xy\geq(x+y)^{2}-\frac{(x+y)^{2}}{4}=\frac{3(x+y)^{2}}{4}\Rightarrow \left| {x+y} \right|\leq 4$\Rightarrow S=x+y\
leq 4
Dau "=" xay ra \Leftrightarrow $x=y=2