设x,y是实数,且x^2+xy+y^2=1,求x^2-xy+y^2的取值范围

楼上的不对,因为取-1的条件是x=y=0,而此时x^2+xy+y^2=1不成立.x^2-xy+y^2＝x^2+xy+y^2-2xy=1-2xyx^2+xy+y^2=1 ≥3xyxy ≤1/3-2xy≥-2/3,x^2-xy+y^2＝x^2+xy+y^2-2xy=1-2xy≥1/3当且仅当 x=y时取等号...