Question 1209926
<pre>
That crazy notation again!  Why they insist on that, I'll neve know.

(a) Let x, y, and z be positive real numbers.  Find the largest possible value of
{{{sqrt((3x + 5y + 2z)/(6x + 5y + 4z)) + sqrt((2x + 5y + z)/(6x + 5y + 5z)) + sqrt((9x + y + 4z)/(6x + 5y + 4z))}}}

The arithmetic mean of expressions for non-negative numbers always exceeds the
geometric mean except when they are all the same.  So we normalize them by
setting x=y=z= a constant, which may as well be 1.  So we let x=y=z=1 and

{{{sqrt(10/15)+sqrt(8/16)+sqrt(14/15)}}}{{{""=""}}}

{{{sqrt(2/3)+sqrt(1/2)+sqrt(14/15)}}}

That's the largest possible value.

(b) Find {{{z/x}}} if (x,y,z) is a triple that gives the maximum value in Part
(a).

Since (1,1,1) is such a triple {{{z/x=1/1=1}}}.  No?  

Edwin</pre>