The range of values of \(k\) such that the only solution to

\[ a^2 + kab + b^2 = 0 \]

is the trivial solution \( a=b=0 \), is \( k \in (m,n) \).

Find the value of \(m^2+n^2\)?

The title refers to the graph of \(w=f(x,y,z)=x^2+xyz+z^2\); if you can imagine that graph then the answer should come naturally. This has no relevance whatsoever to the answer.

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