设实数x,y满足3x^2+2y^2=6,x^2+y^2的取值范围
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设实数x,y满足3x^2+2y^2=6,x^2+y^2的取值范围
设实数x,y满足3x^2+2y^2=6,x^2+y^2的取值范围
设实数x,y满足3x^2+2y^2=6,x^2+y^2的取值范围
由3x^2+2y^2=6得x^2+2x^2+2y^2=6 x^2+2(x^2+y^2)=6
∴2(x^2+y^2)=6- x^2
x^2+y^2=-1/2 x^2+3≤3
又∵3(x^2+y^2)=6+y^2 x^2+y^2=1/3y^2+2≥2
∴2≤x^2+y^2≤3
三角换元即可
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