若x^2 +xy+ y^2=1,x,y∈ R,则n=x^2 +y^2的取值范围是
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因为x^2+2xy+y^2≥0,所以2x^2+2xy+2y^2≥x^2+y^2,即2(x^2+xy+y^2)≥x^2+y^2,而x^2+xy+y^2=1,所以x^2+y^2≤2,又因为1-(x^2+y^2)=xy,而2xy≤x^2+y^2,所以2-2(x^2+y^2)≤x^2+y^2,即x^2+y^2≥2/3,综上得2/3≤x^2+y^2≤2
若x^2 +xy+ y^2=1,x,y∈ R,则n=x^2 +y^2的取值范围是
因为x^2+2xy+y^2≥0,所以2x^2+2xy+2y^2≥x^2+y^2,即2(x^2+xy+y^2)≥x^2+y^2,而x^2+xy+y^2=1,所以x^2+y^2≤2,又因为1-(x^2+y^2)=xy,而2xy≤x^2+y^2,所以2-2(x^2+y^2)≤x^2+y^2,即x^2+y^2≥2/3,综上得2/3≤x^2+y^2≤2