optimization - Lagrange Multipliers to find the maximum and minimum values - Mathematics Stack Exchange

Using Lagrange Multipliers I need to find the maximum and minimum values of the function $f(x,y,z)=x^2+y^2+z^2$ subject to the given constraints: $g(x)= x^2/\alpha^2 +y^2/\beta^2 +z^2/\gamma^2=1$ and

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