Optimize f(x,y,z) = x2 + y2 + z2 - 2x

[squenshl]

Optimize f(x,y,z) = x² + y² + z² - 2x subject to the constraint g(x,y,z) = x² + y² + z² - 25 = 0

Step 1:
L = f - \lambdag = x² + y² + z² - 2x - \lambda(x² + y² + z² - 25).

Step 2:
L_x = 2x - 2 - 2\lambdax = 0
L_y = 2y - 2\lambday = 0
L_z = 2z - 2\lambdaz = 0

What do I do now? Please help.

 

[Office_Shredder]

I see four equations and four unknowns (don't forget that g(x,y,z)=0 gives you another equation!). Have you tried solving for those unknowns?