Find the max and min distance from the origin to the ellipse x^2+xy+y^2=3

Use x^2+y^2 as your objective function.

I tried to do this by using x^2+xy+y^2=3 as my constraint but it doesn't give me the right answer. I can't check the qualification of the constraint because there is an X and a Y when I take partial deriviative of that function. I don't know what to do..

thanks alot