Finding maximum and minimum value

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The discussion focuses on finding the maximum and minimum values of the expression xz + xy - yz under the constraint x^2 + y^2 + z^2 = 1. A user mentions simplifying the problem but seeks further guidance on the next steps. The suggestion to use Lagrange multipliers is provided as a potential method for solving the problem. Ultimately, the user successfully completes the task after receiving assistance. The conversation highlights the utility of Lagrange multipliers in optimization problems with constraints.
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Homework Statement



We have x^2+y^2+z^2=1, and we want to find the maximum and minimum value of xz+xy-yz.

Homework Equations





The Attempt at a Solution


I've simplified the original problem to this point, but I'm not sure what to do next. Could anyone give me some hints? Any help is greatly appreciated!
 
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Thanks a lot! I finished it already:p
 

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