Solving System of Equations - Critical Points

[CoolDude420]

Homework Statement

[/B]
Hi,
I seem to have this issue with solving the a system of 3 equations when trying to find the critical points for a 3 variable function.

Homework Equations

The Attempt at a Solution

It always keeps happening. I keep getting stuck when solving these equations. Every single question has its own little trick in it on how to solve these equations

Any ideas? I need to do this as the first part in solving my question. I need to find the critical points then use the second derivative test to determine the type of critical points. I keep going around and around with equations, trying to fit them into other ones and it leads me nowhere.

 

[timetraveller123]

why is it that in your working
yz = 1/(2 x^2) becomes y = z/(2 x^2)
similarly
xz = 1 /(y^2) becomes x=z/(y^2)
and
xy=2/z^2 becomes x = 2y/z^2

it it that i am missing something or is it did you make a mistake?

 

[Ray Vickson]

why is it that in your working
yz = 1/(2 x^2) becomes y = z/(2 x^2)
similarly
xz = 1 /(y^2) becomes x=z/(y^2)
and
xy=2/z^2 becomes x = 2y/z^2

it it that i am missing something or is it did you make a mistake?

They are all mistakes.

 

[CoolDude420]

They are all mistakes.

Oops. seems like i forgot some basic algebra. Give me a second ill fix that up.