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
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 -4$Dau "=" 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