Finding extreme values using Lagrange Multipliers

Question

So the question asked to find the extreme values of the function $$f(x,y,z)=e^{xyz} $$ under the constraint $$ 2x^2+y^2+z^2=24$$

My attempt :

I'm a bit lost on what to do now, because I tried isolating for one of the variables and sub it back into another one of those 4 equations. But, it only made things messier.

Answer 1

Try dividing the equations by one another. You should be able to find that:

$$y^2 = 2x^2, z^2 = 2x^2, y^2 = z^2$$

Then put them into equation 4 to get each value.