Question

x^2+ xy + y^2 =3 ,求函数 x^2 - xy + y^2 值域

Answer 1

x^2+y^2=3-xy x^2+y^2>=2xy 所以3-xy>=2xy xy=-2 x^2-xy+y^2=x^2+xy+y^2-2xy=3-2xy>=3-2=1 即x^2-xy+y^2>=1 又(x+y)^2>=0,所以x^2y^2>=-2xy 所以3-xy>=-2xy xy>=-3 -2xy