Use Lagrange multiplier to find absolute maximum and minimum Use Lagrange multiplier to find absolute maximum and minimum of $f(x,y) =x^2+xy+y^2, x^2+y^2 =8$. 
What i've done so far..  
$f_x = \lambda g_x \Rightarrow 2x+y =\lambda2x, \\f_y = \lambda g_y \Rightarrow x+2y = \lambda 2y,\\g(x,y) = x^2+y^2 -8 =0$ 
May I know how should i proceed from here?

On a side note, this problem can be solved very nicely with substitution since it's equivalent to:
$$f(\theta) = 8 \left ( 1 + \frac{1}{2}\sin 2\theta \right )$$
where $ x = r \cos\theta$, $y = r \sin \theta$ and $r = 2\sqrt{2}$.
Since $f(\theta)$ is the same as maximizing $\sin 2 \theta$, $f(\theta)$ is maximum and minimum at $\theta = \pi n + \frac{\pi}{4}$ and $\theta = \pi n - \frac{\pi}{4}$ respectively.
So if $n = 1$, we have a maximum at $x = -2, y = -2$ and a minimum at $x = -2, y = 2$.
