已知实数x,y满足3x^2+2y^2=6x,则x^2+y^2的最大值是?

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已知实数x,y满足3x^2+2y^2=6x,则x^2+y^2的最大值是?已知实数x,y满足3x^2+2y^2=6x,则x^2+y^2的最大值是?已知实数x,y满足3x^2+2y^2=6x,则x^2+y

已知实数x,y满足3x^2+2y^2=6x,则x^2+y^2的最大值是?
已知实数x,y满足3x^2+2y^2=6x,则x^2+y^2的最大值是?

已知实数x,y满足3x^2+2y^2=6x,则x^2+y^2的最大值是?
已知3x^2+2y^2 = 6x
则y^2 = 3x - 3/2 x^2
x^2+y^2
=x^2 + 3x - 3/2 x^2
= - 1/2 x^2 + 3x
配方
= -1/2(x-3)^2 + 9/2
-1/2(x-3)^2 <= 0
所以最大值为
9/2