Back To Basics II

Algebra Level 5

x,y,x,y, and zz are real numbers satisfying the equation x2+y2+z2=1.x^{2}+y^{2}+z^{2}=1.

The maximum value of 3xy2z3xy^{2}z can be expressed in the form ab\dfrac{a}{b} for co-prime positive integers aa and bb.

Find a+ba+b.


Bonus:

Can you generalize the maximum value of xmynzpx^{m}y^{n}z^{p} for positive integers m,n,pm,n,p given the same constraints?

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