若实数x、y满足2x^2+3y^2=1,s=3x^2-2y^2,则S的取值范围是

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若实数x、y满足2x^2+3y^2=1,s=3x^2-2y^2,则S的取值范围是
若实数x、y满足2x^2+3y^2=1,s=3x^2-2y^2,则S的取值范围是

若实数x、y满足2x^2+3y^2=1,s=3x^2-2y^2,则S的取值范围是
因为2x^2+3y^2=1,则x^2=(1-3y^2)/2
则s=3x^2-2y^2=3(1-3y^2)/2 -2y^2=3/2 -5y^2/2
又因为2x^2+3y^2=1,0≤y^2= (1-2x^2)/3≤1/3
则有s=3/2 -5y^2/2 ∊ [2/3,3/2 ]
即y=0,取最大值3/2
y=1/3,取最小值 3/2 - 5/6 =4/6=2/3

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