已知实数x,y满足x2+xy+y2=3,则x2-xy+y2的最小值

已知实数x,y满足x2+xy+y2=3,则x2-xy+y2的最小值
已知实数x,y满足x2+xy+y2=3,则x2-xy+y2的最小值

已知实数x,y满足x2+xy+y2=3,则x2-xy+y2的最小值
由x2+xy+y2=3得,
x^2+y^2=3-xy
x^2+y^2 ≥ 2xy得,xy≤1
所以
x^2-xy+y^2=3-2xy≥1
等号成立当且仅当x=y=±1