若x,y满足3x^2+2y^2=6x,求z=x^2+y^2值域

问题描述:

若x,y满足3x^2+2y^2=6x,求z=x^2+y^2值域

3x^2+2y^2=6x
6x>=0
x>=0
3x^2+2y^2=6x
2x^2+2y^2=-x^2+6x
x^2+y^2=-x^2+6x/2
z=x^2+y^2
z=-x^2+6x/2=-1/2(x^2-6x+9-9)
=-1/2(x-3)^2+9/2