3x^2+2y^2=2x
y^2=x-1.5x^2
x^2+y^2=x-1.5x^2+x^2=-0.5x^2+x=-0.5(x^2-2x+1)+0.5
=-0.5(x-1)^2+0.5
当x=1时,x^2+y^2最大值0.5