I need help on the following problem:

Find the absolute maximum and minimum of the function $\displaystyle f(x,y) = x^2 + y^2 $ subject to the constraint $\displaystyle x^4 + y^4 = 625 $.

I tried using Lagrange's multiplier to this problem but here is where I'm stuck.

$\displaystyle \frac{\partial f}{\partial x}= \lambda\frac{\partial g}{\partial x}$

$\displaystyle 2x = 4x^3 \lambda $

$\displaystyle \frac{\partial f}{\partial y} = \lambda\frac{\partial g}{\partial y}$

$\displaystyle 2y = 4y^3\lambda $

I just can't seem to be able to solve for $\displaystyle x,y, \lambda $,which I need for the critical points