# Inspired by Brian Charlesworth, again

Algebra Level 5

$10xy+12xz+14yz$

Let $$M$$ and $$m$$ be the maximum and the minimum of the expression above if $$x^2+y^2+z^2=1$$, where $$x,y$$ and $$z$$ are real numbers. Find $$M^2+Mm+m^2$$.

Bonus question: For $$2axy+2bxz+2cyz$$, with the same constraint, express $$M^2+Mm+m^2$$ in terms of $$a,b$$ and $$c$$.

Inspiration

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