LaGrange Multiplier Problem

I'm trying to find the minimum and maximum values of

$\displaystyle f(x,y,z,) = (4x - 1/2y + 27/2 z)$

on the surface of $\displaystyle g=x^4+y^4+z^4=1$

I have already put $\displaystyle \bigtriangledown f = \lambda \bigtriangledown g $

Getting the following 4 equations... Where do I go from here?

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

$\displaystyle 4\lambda y^3=-1/2$

$\displaystyle 4\lambda z^3=27/2$

$\displaystyle x^4+y^4+z^4=1$

I know I need to solve...

There are 4 unknowns (counting **λ**) but variables x, y, z are raised to the power of 4.

I don't know how to solve this system... Any help?