1已知3(x-1)^2+2y^2=3,求x^2+y^2的最大值和最小值

1已知3(x-1)^2+2y^2=3,求x^2+y^2的最大值和最小值
1已知3(x-1)^2+2y^2=3,求x^2+y^2的最大值和最小值

1已知3(x-1)^2+2y^2=3,求x^2+y^2的最大值和最小值
(x-1)^2+(2/3)y^2=1
令(x-1)^2=(sina)^2
(2/3)y^2=(cosa)^2
则y^2=(3/2)(cosa)^2
x=1+|sina|或x=1-|sina|
x^2=1+sina^2+2sina或x^2=1+sina^2-2sina
x^2+y^2
=(3/2)(cosa)^2+1+sina^2+2sina
=(1/2)[1-(sina)^2]+2+2sina
=-1/2(sina)^2+2sina+5/2
=(-1/2)(sina-2)^2+9/2
sina=-1时,有最小值0
sina=1时,有最大值4
x^2+y^2
=(3/2)(cosa)^2+1+sina^2-2sina
=(1/2)[1-(sina)^2]+2-2sina
=-1/2(sina)^2-2sina+5/2
=(-1/2)(sina+2)^2+9/2
sina=1时,有最小值0
sina=-1时,有最大值4
综上,x^2+y^2最大值为4,最小值为0.