All you need is a 4d imagination
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.