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
Most of a solution by Brian Smith)
absolutely correct. This very similar to the method I had proposed but my lack of mathematical programs caused me to lose interest in carrying through to a full solution. This is not a fun derivative to solve by hand, especially when you consider that there must be 4 cases to check (combinations of 2 roots for x and two roots for z). I tried it a few times, but my carelessness showed up as mistakes that haunted me.
From my shots at this however, I seem to remember that the maximum appeared at two places (both yielding A=8), but it could just be fake memory. Whether this requires a change to the y value I don't recall for sure (I don't *think* it did), but the values for x and z did change.
I suppose that you still need to solve for these two variables and maybe the duplicity will show upo there.
re: Most of a solution
