We have :

x^2+xy+y^2=3 and
y^2+yz+z^2=16
A=xy+yz+zx

Find the maximum value of

**A**.
Find x, y and z when A=max value.

(Remember the category)

(In reply to

re: Most of a solution by Cory Taylor)

Its nice to see i am not alone in tackling this problem.

With how bad the equations get, I was looking to find any solution first.

x=2/sqrt(31) y=4/sqrt(31) z=7/sqrt(31) A=8 is the only solution I have so far, but I restricted the values to positive integers to help get a handle on this thing.