All you need is a 4d imagination

Algebra Level 4

The range of values of kk such that the only solution to

a2+kab+b2=0 a^2 + kab + b^2 = 0

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

Find the value of m2+n2m^2+n^2?

The title refers to the graph of w=f(x,y,z)=x2+xyz+z2w=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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