# Playing with the Glome

Algebra Level 5

$2xy+4yz+6zw$

Let $$M$$ be the maximum of the expression above if $$x^2+y^2+z^2+w^2=1$$, where $$x,y,z$$ and $$w$$ are real numbers. Write $$M=\sqrt{p}+\sqrt{q}$$ for two positive integers $$p$$ and $$q$$, and enter $$p+q$$.

Bonus question: For $$axy+byz+czw$$, with the same constraint, express the maximum $$M$$ in terms of $$a,b$$ and $$c$$.

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