As per request from Comrade Pi Han Goh

Algebra Level 5

$\begin{eqnarray} f_a(x,y,z)&=&ax^2+(a+1)y^2+(a+2)z^2 \\ && -4xy-4yz+2x-3y+4z-5 \end{eqnarray}$

Find the smallest real number $$a$$ such that the function $$f_a(x,y,z)$$ has a (global) minimum.

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