This question is not part of my course (I do Economics) or probably at my capabilities as of yet. But I wish to have a greater understanding of 3D geometry (I believe that is the area). I received this question from a bonus question from a summer exam paper and am seeking help with it. So without further ado..
minimum value for $x^2 + y^2 + z^2$ where $x, y, z$ are real numbers such that $x^3 + y^3 + z^3 - 3xyz = 1$
Thank you for any help!
P.S. Is my constraint $x^2 + y^2 + z^2$??
P.S.S. Nevermind
P.S.S.S. So after finding critical points I plugged them back into the function, I got roughly 0.11791 as my lowest value, unsure if this is correct.