lagrange multiplier stuck

[ratho]

problem: use lagrange multipliers to find the maximum and minimum values of f(x)= x+y+z along the intersection of the constraints g(x) x^2-y^2 =z and (h) x^2+z^2=4..

first question for the constraint g(x) do i need to bring the Z across to make the eqn x^2-y^2-z=0 ?

here is what i have for the problem so far.

(fx) 1=2xλ+2xµ
(fy) 1= -2yλ >>>>>>>>>y= -1/2λ
f(z) 1= - λ +2zµ >>>>>>z = λ / 2µ

stuck here not sure how to solve for any value x or y or z so i can continue any help would be greatly appreciated.
sorry for the bad English if i miss typed.

 

[ratho]

thank you for the fast replay but just to make sure im understanding it correct i am to use the Jx,Jy,Jz to solve for lambda first then mew and that way i can find the values for X,Y,Z?.. sorry this problem is making me nuts.

 

[ratho]

hate to ask again in here but i cant solve this thing at all i have been at it for three days with the help of an online tutor and they cant solve it... i really dont want to seem like im asking you to solve my homework but im out of options so if anyone can do this problem please help or at least point me in the right direction thank you.