# All you need is a 4d imagination

Algebra Level 4

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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